Answer
$34650$
Work Step by Step
In "MISSISSIPPI", there are 1 M, 4 I's, 4 S's, and 2 P's, for a total of 11 letters. So we are trying to calculate the number of permutations of 11 letters, with the 4 I's indistinguishable from each other, 4 S's indistinguishable from each other, and 2 P's indistinguishable from each other. By Theorem 3 on page 428, the number of permutations is:
$\frac{11!}{4!4!2!}$
$=\frac{1*2*3*4*5*6*7*8*9*10*11}{1*2*3*4*1*2*3*4*1*2}$
$=\frac{5*6*7*8*9*10*11}{1*2*3*4*1*2}$
$=34650$
