Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N...
Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together
This is my working-
$3! cdot frac{7!}{2!} $
is this correct ?
combinatorics
asked Nov 24 at 14:55
mutu mumu
374
closed as off-topic by Don Thousand, MisterRiemann, NCh, Shailesh, John B Dec 1 at 0:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Don Thousand, MisterRiemann, NCh, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together
This is my working-
$3! cdot frac{7!}{2!} $
is this correct ?
combinatorics
asked Nov 24 at 14:55
mutu mumu
374
closed as off-topic by Don Thousand, MisterRiemann, NCh, Shailesh, John B Dec 1 at 0:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Don Thousand, MisterRiemann, NCh, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
5
Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
– MisterRiemann
Nov 24 at 15:00
1
Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
– N. F. Taussig
Nov 24 at 15:04
add a comment |
Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together
This is my working-
$3! cdot frac{7!}{2!} $
is this correct ?
combinatorics
asked Nov 24 at 14:55
mutu mumu
374
Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together
This is my working-
$3! cdot frac{7!}{2!} $
is this correct ?
combinatorics
combinatorics
asked Nov 24 at 14:55
mutu mumu
374
asked Nov 24 at 14:55
mutu mumu
374
asked Nov 24 at 14:55
mutu mumu
374
asked Nov 24 at 14:55
mutu mumu
374
asked Nov 24 at 14:55
mutu mumu
374
374
closed as off-topic by Don Thousand, MisterRiemann, NCh, Shailesh, John B Dec 1 at 0:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Don Thousand, MisterRiemann, NCh, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Don Thousand, MisterRiemann, NCh, Shailesh, John B Dec 1 at 0:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Don Thousand, MisterRiemann, NCh, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
5
Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
– MisterRiemann
Nov 24 at 15:00
1
Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
– N. F. Taussig
Nov 24 at 15:04
add a comment |
5
Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
– MisterRiemann
Nov 24 at 15:00
1
Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
– N. F. Taussig
Nov 24 at 15:04
5
5
Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
– MisterRiemann
Nov 24 at 15:00
Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
– MisterRiemann
Nov 24 at 15:00
1
1
Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
– N. F. Taussig
Nov 24 at 15:04
Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
– N. F. Taussig
Nov 24 at 15:04
add a comment |
3 Answers
3
active
oldest
votes
Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.
answered Nov 24 at 16:52
priyanka kumari
1297
add a comment |
I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:
- Can you explain your working for getting the 7!, 3! and 2! ?
- Will using 7! include the possibilities where T, E, N are together but are located elsewhere?
- In how many positions can the group of three letters be placed together?
- Does using 7! account for all of these positions?
Perhaps these questions will lead you to the correct solution.
answered Nov 24 at 15:15
Danila Kurganov
112
add a comment |
Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.
So total number of ways is $dfrac{8!cdot 3!}{2!}$.
answered Nov 24 at 15:48
Yadati Kiran
1,694619
@N.F.Taussig: Sorry. My bad.
– Yadati Kiran
Nov 24 at 16:07
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.
answered Nov 24 at 16:52
priyanka kumari
1297
add a comment |
Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.
answered Nov 24 at 16:52
priyanka kumari
1297
add a comment |
Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.
answered Nov 24 at 16:52
priyanka kumari
1297
Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.
answered Nov 24 at 16:52
priyanka kumari
1297
answered Nov 24 at 16:52
priyanka kumari
1297
answered Nov 24 at 16:52
priyanka kumari
1297
answered Nov 24 at 16:52
priyanka kumari
1297
1297
add a comment |
add a comment |
I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:
- Can you explain your working for getting the 7!, 3! and 2! ?
- Will using 7! include the possibilities where T, E, N are together but are located elsewhere?
- In how many positions can the group of three letters be placed together?
- Does using 7! account for all of these positions?
Perhaps these questions will lead you to the correct solution.
answered Nov 24 at 15:15
Danila Kurganov
112
add a comment |
I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:
- Can you explain your working for getting the 7!, 3! and 2! ?
- Will using 7! include the possibilities where T, E, N are together but are located elsewhere?
- In how many positions can the group of three letters be placed together?
- Does using 7! account for all of these positions?
Perhaps these questions will lead you to the correct solution.
answered Nov 24 at 15:15
Danila Kurganov
112
add a comment |
I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:
- Can you explain your working for getting the 7!, 3! and 2! ?
- Will using 7! include the possibilities where T, E, N are together but are located elsewhere?
- In how many positions can the group of three letters be placed together?
- Does using 7! account for all of these positions?
Perhaps these questions will lead you to the correct solution.
answered Nov 24 at 15:15
Danila Kurganov
112
I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:
- Can you explain your working for getting the 7!, 3! and 2! ?
- Will using 7! include the possibilities where T, E, N are together but are located elsewhere?
- In how many positions can the group of three letters be placed together?
- Does using 7! account for all of these positions?
Perhaps these questions will lead you to the correct solution.
answered Nov 24 at 15:15
Danila Kurganov
112
answered Nov 24 at 15:15
Danila Kurganov
112
answered Nov 24 at 15:15
Danila Kurganov
112
answered Nov 24 at 15:15
Danila Kurganov
112
112
add a comment |
add a comment |
Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.
So total number of ways is $dfrac{8!cdot 3!}{2!}$.
answered Nov 24 at 15:48
Yadati Kiran
1,694619
@N.F.Taussig: Sorry. My bad.
– Yadati Kiran
Nov 24 at 16:07
add a comment |
Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.
So total number of ways is $dfrac{8!cdot 3!}{2!}$.
answered Nov 24 at 15:48
Yadati Kiran
1,694619
@N.F.Taussig: Sorry. My bad.
– Yadati Kiran
Nov 24 at 16:07
add a comment |
Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.
So total number of ways is $dfrac{8!cdot 3!}{2!}$.
answered Nov 24 at 15:48
Yadati Kiran
1,694619
Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.
So total number of ways is $dfrac{8!cdot 3!}{2!}$.
answered Nov 24 at 15:48
Yadati Kiran
1,694619
edited Nov 24 at 16:09
answered Nov 24 at 15:48
Yadati Kiran
1,694619
answered Nov 24 at 15:48
Yadati Kiran
1,694619
answered Nov 24 at 15:48
Yadati Kiran
1,694619
1,694619
@N.F.Taussig: Sorry. My bad.
– Yadati Kiran
Nov 24 at 16:07
add a comment |
@N.F.Taussig: Sorry. My bad.
– Yadati Kiran
Nov 24 at 16:07
@N.F.Taussig: Sorry. My bad.
– Yadati Kiran
Nov 24 at 16:07
@N.F.Taussig: Sorry. My bad.
– Yadati Kiran
Nov 24 at 16:07
add a comment |
5
Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
– MisterRiemann
Nov 24 at 15:00
1
Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
– N. F. Taussig
Nov 24 at 15:04