Given 20 sugar bars and 50 salt bars. Consider subsets of these 70 bars, consisting of 30 bars, exactly 12...












0














Question: You are given 20 sugar bars (B1,B2,..B20) and 50 salt bars (S1, S2..S50). Consider subsets of these 70 bars, consisting of 30 bars, exactly 12 of which are sugar bars. How many such subsets are there? (Answer: 2.2742 * 10^18)



Attempt: The consisting of 30 bars part confuses me. Like, am I supposed to find the subset of a subset here? From 70 total bars, a subset of 30 bars where there are 12 sugar bars and therefore 18 salt bars exist. So, I'm assuming I use combinations here? Am I finding the number of subsets that consist of 30 bars with 12 being sugar bars and a different combination of salt bars?



What if the question was asking You are given 20 sugar bars (B1,B2,..B20) and 50 salt bars (S1, S2..S50). Consider subsets of these 70 bars, that contain at least 3 of which are sugar bars (and any number of salt bars). How many such subsets are there?



What would the difference in approach be when the wording changes from "exactly" to "at least"






combinatorics permutations







share|cite|improve this question


















  • 1




    Choose 12 out of 20 sugar bars (expression using combinations) then choose 18 out of 50 salt, another combination. Then multiply them together as the choices are independent
    – Gordon Royle
    Nov 25 at 1:49










  • Why talking about sugar bars instead of girls? For all practical purposes there is just one such subset.
    – Christian Blatter
    Nov 25 at 8:57
















0














Question: You are given 20 sugar bars (B1,B2,..B20) and 50 salt bars (S1, S2..S50). Consider subsets of these 70 bars, consisting of 30 bars, exactly 12 of which are sugar bars. How many such subsets are there? (Answer: 2.2742 * 10^18)



Attempt: The consisting of 30 bars part confuses me. Like, am I supposed to find the subset of a subset here? From 70 total bars, a subset of 30 bars where there are 12 sugar bars and therefore 18 salt bars exist. So, I'm assuming I use combinations here? Am I finding the number of subsets that consist of 30 bars with 12 being sugar bars and a different combination of salt bars?



What if the question was asking You are given 20 sugar bars (B1,B2,..B20) and 50 salt bars (S1, S2..S50). Consider subsets of these 70 bars, that contain at least 3 of which are sugar bars (and any number of salt bars). How many such subsets are there?



What would the difference in approach be when the wording changes from "exactly" to "at least"






combinatorics permutations







share|cite|improve this question


















  • 1




    Choose 12 out of 20 sugar bars (expression using combinations) then choose 18 out of 50 salt, another combination. Then multiply them together as the choices are independent
    – Gordon Royle
    Nov 25 at 1:49










  • Why talking about sugar bars instead of girls? For all practical purposes there is just one such subset.
    – Christian Blatter
    Nov 25 at 8:57














0












0








0







Question: You are given 20 sugar bars (B1,B2,..B20) and 50 salt bars (S1, S2..S50). Consider subsets of these 70 bars, consisting of 30 bars, exactly 12 of which are sugar bars. How many such subsets are there? (Answer: 2.2742 * 10^18)



Attempt: The consisting of 30 bars part confuses me. Like, am I supposed to find the subset of a subset here? From 70 total bars, a subset of 30 bars where there are 12 sugar bars and therefore 18 salt bars exist. So, I'm assuming I use combinations here? Am I finding the number of subsets that consist of 30 bars with 12 being sugar bars and a different combination of salt bars?



What if the question was asking You are given 20 sugar bars (B1,B2,..B20) and 50 salt bars (S1, S2..S50). Consider subsets of these 70 bars, that contain at least 3 of which are sugar bars (and any number of salt bars). How many such subsets are there?



What would the difference in approach be when the wording changes from "exactly" to "at least"






combinatorics permutations







share|cite|improve this question













Question: You are given 20 sugar bars (B1,B2,..B20) and 50 salt bars (S1, S2..S50). Consider subsets of these 70 bars, consisting of 30 bars, exactly 12 of which are sugar bars. How many such subsets are there? (Answer: 2.2742 * 10^18)



Attempt: The consisting of 30 bars part confuses me. Like, am I supposed to find the subset of a subset here? From 70 total bars, a subset of 30 bars where there are 12 sugar bars and therefore 18 salt bars exist. So, I'm assuming I use combinations here? Am I finding the number of subsets that consist of 30 bars with 12 being sugar bars and a different combination of salt bars?



What if the question was asking You are given 20 sugar bars (B1,B2,..B20) and 50 salt bars (S1, S2..S50). Consider subsets of these 70 bars, that contain at least 3 of which are sugar bars (and any number of salt bars). How many such subsets are there?



What would the difference in approach be when the wording changes from "exactly" to "at least"






combinatorics permutations




combinatorics permutations






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 25 at 1:36









Toby

1577




1577








  • 1




    Choose 12 out of 20 sugar bars (expression using combinations) then choose 18 out of 50 salt, another combination. Then multiply them together as the choices are independent
    – Gordon Royle
    Nov 25 at 1:49










  • Why talking about sugar bars instead of girls? For all practical purposes there is just one such subset.
    – Christian Blatter
    Nov 25 at 8:57














  • 1




    Choose 12 out of 20 sugar bars (expression using combinations) then choose 18 out of 50 salt, another combination. Then multiply them together as the choices are independent
    – Gordon Royle
    Nov 25 at 1:49










  • Why talking about sugar bars instead of girls? For all practical purposes there is just one such subset.
    – Christian Blatter
    Nov 25 at 8:57








1




1




Choose 12 out of 20 sugar bars (expression using combinations) then choose 18 out of 50 salt, another combination. Then multiply them together as the choices are independent
– Gordon Royle
Nov 25 at 1:49




Choose 12 out of 20 sugar bars (expression using combinations) then choose 18 out of 50 salt, another combination. Then multiply them together as the choices are independent
– Gordon Royle
Nov 25 at 1:49












Why talking about sugar bars instead of girls? For all practical purposes there is just one such subset.
– Christian Blatter
Nov 25 at 8:57




Why talking about sugar bars instead of girls? For all practical purposes there is just one such subset.
– Christian Blatter
Nov 25 at 8:57










1 Answer
1






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you're working with 70 bars, 50 salty and 20 sugary. We only care about the subsets that have 12 sugary, it could be any 12 from the total 20 that are sugary so we have a combination ${20}choose{12}$ that lets us know all the possible combinations of 12 bars that we can work with. Since we're only interested in the subsets with 30 bars in total we have to have 18 salty bars. But similarly we want all possible combinations of the 18 from 50, so we end up with ${50}choose{18}$. The product ${20}choose{12}$${50}choose{18}$ gives us the answer. If we were to say that the subsets have to have at "least" 12, we would have to add the products of the different combinations , ${20}choose{12}$${50}choose{18}$+${20}choose{13}$${50}choose{17}$+ $cdots$ +${20}choose{20}$${50}choose{10}$






share|cite|improve this answer























  • Since there a total of $30$ bars in the subset, if we select $20$ sugar bars, how many salt bars must we select?
    – N. F. Taussig
    Nov 25 at 3:03










  • my bad, let me edit my response
    – Javi maxwell
    Nov 25 at 5:21










  • In the problem posed by the OP, the question asks for selections with at least $3$ sugar bars, which allows the more efficient solution of subtracting those selections with fewer than three sugar bars from the total. However, your response is clear and helpful. Welcome to the site.
    – N. F. Taussig
    Nov 25 at 10:20











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you're working with 70 bars, 50 salty and 20 sugary. We only care about the subsets that have 12 sugary, it could be any 12 from the total 20 that are sugary so we have a combination ${20}choose{12}$ that lets us know all the possible combinations of 12 bars that we can work with. Since we're only interested in the subsets with 30 bars in total we have to have 18 salty bars. But similarly we want all possible combinations of the 18 from 50, so we end up with ${50}choose{18}$. The product ${20}choose{12}$${50}choose{18}$ gives us the answer. If we were to say that the subsets have to have at "least" 12, we would have to add the products of the different combinations , ${20}choose{12}$${50}choose{18}$+${20}choose{13}$${50}choose{17}$+ $cdots$ +${20}choose{20}$${50}choose{10}$






share|cite|improve this answer























  • Since there a total of $30$ bars in the subset, if we select $20$ sugar bars, how many salt bars must we select?
    – N. F. Taussig
    Nov 25 at 3:03










  • my bad, let me edit my response
    – Javi maxwell
    Nov 25 at 5:21










  • In the problem posed by the OP, the question asks for selections with at least $3$ sugar bars, which allows the more efficient solution of subtracting those selections with fewer than three sugar bars from the total. However, your response is clear and helpful. Welcome to the site.
    – N. F. Taussig
    Nov 25 at 10:20
















1














you're working with 70 bars, 50 salty and 20 sugary. We only care about the subsets that have 12 sugary, it could be any 12 from the total 20 that are sugary so we have a combination ${20}choose{12}$ that lets us know all the possible combinations of 12 bars that we can work with. Since we're only interested in the subsets with 30 bars in total we have to have 18 salty bars. But similarly we want all possible combinations of the 18 from 50, so we end up with ${50}choose{18}$. The product ${20}choose{12}$${50}choose{18}$ gives us the answer. If we were to say that the subsets have to have at "least" 12, we would have to add the products of the different combinations , ${20}choose{12}$${50}choose{18}$+${20}choose{13}$${50}choose{17}$+ $cdots$ +${20}choose{20}$${50}choose{10}$






share|cite|improve this answer























  • Since there a total of $30$ bars in the subset, if we select $20$ sugar bars, how many salt bars must we select?
    – N. F. Taussig
    Nov 25 at 3:03










  • my bad, let me edit my response
    – Javi maxwell
    Nov 25 at 5:21










  • In the problem posed by the OP, the question asks for selections with at least $3$ sugar bars, which allows the more efficient solution of subtracting those selections with fewer than three sugar bars from the total. However, your response is clear and helpful. Welcome to the site.
    – N. F. Taussig
    Nov 25 at 10:20














1












1








1






you're working with 70 bars, 50 salty and 20 sugary. We only care about the subsets that have 12 sugary, it could be any 12 from the total 20 that are sugary so we have a combination ${20}choose{12}$ that lets us know all the possible combinations of 12 bars that we can work with. Since we're only interested in the subsets with 30 bars in total we have to have 18 salty bars. But similarly we want all possible combinations of the 18 from 50, so we end up with ${50}choose{18}$. The product ${20}choose{12}$${50}choose{18}$ gives us the answer. If we were to say that the subsets have to have at "least" 12, we would have to add the products of the different combinations , ${20}choose{12}$${50}choose{18}$+${20}choose{13}$${50}choose{17}$+ $cdots$ +${20}choose{20}$${50}choose{10}$






share|cite|improve this answer














you're working with 70 bars, 50 salty and 20 sugary. We only care about the subsets that have 12 sugary, it could be any 12 from the total 20 that are sugary so we have a combination ${20}choose{12}$ that lets us know all the possible combinations of 12 bars that we can work with. Since we're only interested in the subsets with 30 bars in total we have to have 18 salty bars. But similarly we want all possible combinations of the 18 from 50, so we end up with ${50}choose{18}$. The product ${20}choose{12}$${50}choose{18}$ gives us the answer. If we were to say that the subsets have to have at "least" 12, we would have to add the products of the different combinations , ${20}choose{12}$${50}choose{18}$+${20}choose{13}$${50}choose{17}$+ $cdots$ +${20}choose{20}$${50}choose{10}$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Nov 25 at 5:22

























answered Nov 25 at 2:06









Javi maxwell

264




264












  • Since there a total of $30$ bars in the subset, if we select $20$ sugar bars, how many salt bars must we select?
    – N. F. Taussig
    Nov 25 at 3:03










  • my bad, let me edit my response
    – Javi maxwell
    Nov 25 at 5:21










  • In the problem posed by the OP, the question asks for selections with at least $3$ sugar bars, which allows the more efficient solution of subtracting those selections with fewer than three sugar bars from the total. However, your response is clear and helpful. Welcome to the site.
    – N. F. Taussig
    Nov 25 at 10:20


















  • Since there a total of $30$ bars in the subset, if we select $20$ sugar bars, how many salt bars must we select?
    – N. F. Taussig
    Nov 25 at 3:03










  • my bad, let me edit my response
    – Javi maxwell
    Nov 25 at 5:21










  • In the problem posed by the OP, the question asks for selections with at least $3$ sugar bars, which allows the more efficient solution of subtracting those selections with fewer than three sugar bars from the total. However, your response is clear and helpful. Welcome to the site.
    – N. F. Taussig
    Nov 25 at 10:20
















Since there a total of $30$ bars in the subset, if we select $20$ sugar bars, how many salt bars must we select?
– N. F. Taussig
Nov 25 at 3:03




Since there a total of $30$ bars in the subset, if we select $20$ sugar bars, how many salt bars must we select?
– N. F. Taussig
Nov 25 at 3:03












my bad, let me edit my response
– Javi maxwell
Nov 25 at 5:21




my bad, let me edit my response
– Javi maxwell
Nov 25 at 5:21












In the problem posed by the OP, the question asks for selections with at least $3$ sugar bars, which allows the more efficient solution of subtracting those selections with fewer than three sugar bars from the total. However, your response is clear and helpful. Welcome to the site.
– N. F. Taussig
Nov 25 at 10:20




In the problem posed by the OP, the question asks for selections with at least $3$ sugar bars, which allows the more efficient solution of subtracting those selections with fewer than three sugar bars from the total. However, your response is clear and helpful. Welcome to the site.
– N. F. Taussig
Nov 25 at 10:20


















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