How many bit strings of length $8$ have $3$ x's in a row?
$begingroup$
A strings of length $8$ using the letters x and y only
1) How many of these strings have exactly $3$ x's? So it's $binom{8}{3} = 56$
2) How many of these strings have 3 x's in a row?
I don't know how to handle that case, so for that one the order matters. So in my opinion it should contain $P(8,3) = 8 times 7 times 6 = 336$. But I should have something to deduct from that, I am confused.
Thank you!
combinatorics discrete-mathematics permutations
edited Dec 2 '18 at 16:37
N. F. Taussig
44k93355
asked Dec 2 '18 at 16:24
Tom1999Tom1999
445
$endgroup$
add a comment |
$begingroup$
A strings of length $8$ using the letters x and y only
1) How many of these strings have exactly $3$ x's? So it's $binom{8}{3} = 56$
2) How many of these strings have 3 x's in a row?
I don't know how to handle that case, so for that one the order matters. So in my opinion it should contain $P(8,3) = 8 times 7 times 6 = 336$. But I should have something to deduct from that, I am confused.
Thank you!
combinatorics discrete-mathematics permutations
edited Dec 2 '18 at 16:37
N. F. Taussig
44k93355
asked Dec 2 '18 at 16:24
Tom1999Tom1999
445
$endgroup$
1
$begingroup$
Easier to count the strings that do not have three $X's $ in a row. Such a string must end in exactly one of $Y,YX, YXX$ (if it has length at least $3$) so you can count these recursively.
$endgroup$
– lulu
Dec 2 '18 at 16:26
$begingroup$
Please read this tutorial on how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 2 '18 at 16:37
add a comment |
$begingroup$
A strings of length $8$ using the letters x and y only
1) How many of these strings have exactly $3$ x's? So it's $binom{8}{3} = 56$
2) How many of these strings have 3 x's in a row?
I don't know how to handle that case, so for that one the order matters. So in my opinion it should contain $P(8,3) = 8 times 7 times 6 = 336$. But I should have something to deduct from that, I am confused.
Thank you!
combinatorics discrete-mathematics permutations
edited Dec 2 '18 at 16:37
N. F. Taussig
44k93355
asked Dec 2 '18 at 16:24
Tom1999Tom1999
445
$endgroup$
A strings of length $8$ using the letters x and y only
1) How many of these strings have exactly $3$ x's? So it's $binom{8}{3} = 56$
2) How many of these strings have 3 x's in a row?
I don't know how to handle that case, so for that one the order matters. So in my opinion it should contain $P(8,3) = 8 times 7 times 6 = 336$. But I should have something to deduct from that, I am confused.
Thank you!
combinatorics discrete-mathematics permutations
combinatorics discrete-mathematics permutations
edited Dec 2 '18 at 16:37
N. F. Taussig
44k93355
asked Dec 2 '18 at 16:24
Tom1999Tom1999
445
edited Dec 2 '18 at 16:37
N. F. Taussig
44k93355
asked Dec 2 '18 at 16:24
Tom1999Tom1999
445
edited Dec 2 '18 at 16:37
N. F. Taussig
44k93355
edited Dec 2 '18 at 16:37
N. F. Taussig
44k93355
edited Dec 2 '18 at 16:37
N. F. Taussig
44k93355
44k93355
asked Dec 2 '18 at 16:24
Tom1999Tom1999
445
asked Dec 2 '18 at 16:24
Tom1999Tom1999
445
asked Dec 2 '18 at 16:24
Tom1999Tom1999
445
445
1
$begingroup$
Easier to count the strings that do not have three $X's $ in a row. Such a string must end in exactly one of $Y,YX, YXX$ (if it has length at least $3$) so you can count these recursively.
$endgroup$
– lulu
Dec 2 '18 at 16:26
$begingroup$
Please read this tutorial on how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 2 '18 at 16:37
add a comment |
1
$begingroup$
Easier to count the strings that do not have three $X's $ in a row. Such a string must end in exactly one of $Y,YX, YXX$ (if it has length at least $3$) so you can count these recursively.
$endgroup$
– lulu
Dec 2 '18 at 16:26
$begingroup$
Please read this tutorial on how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 2 '18 at 16:37
1
1
$begingroup$
Easier to count the strings that do not have three $X's $ in a row. Such a string must end in exactly one of $Y,YX, YXX$ (if it has length at least $3$) so you can count these recursively.
$endgroup$
– lulu
Dec 2 '18 at 16:26
$begingroup$
Easier to count the strings that do not have three $X's $ in a row. Such a string must end in exactly one of $Y,YX, YXX$ (if it has length at least $3$) so you can count these recursively.
$endgroup$
– lulu
Dec 2 '18 at 16:26
$begingroup$
Please read this tutorial on how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 2 '18 at 16:37
$begingroup$
Please read this tutorial on how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 2 '18 at 16:37
add a comment |
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1
$begingroup$
Easier to count the strings that do not have three $X's $ in a row. Such a string must end in exactly one of $Y,YX, YXX$ (if it has length at least $3$) so you can count these recursively.
$endgroup$
– lulu
Dec 2 '18 at 16:26
$begingroup$
Please read this tutorial on how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 2 '18 at 16:37