Solution: 2013 Fall Midterm - 7
Author: Pat MorinQuestion
How many bitstrings of length 13 contain exactly 3 zeros?
(a)
$13!/3!$
(b)
$2^{13} - 3$
(c)
${13}\choose{10}$
(d)
$2^{13} - {{13}\choose{3}}$
Solution
We can choose 3 spots for the zeros out of the 13 spots.
$ \binom{13}{3} $
$ = \binom{13}{10} $