Consider the letters MISSISSIPPI. How many permutations.
a) Begin with P and end with S.
11 letters in all
so, eliminating the P and S, there are 9 remaining.
4 I's, 3 S's
So, 9!/(4!3!) = 2520
Why did you include the S's with the like letters but not the P's?
To find the number of permutations that begin with P and end with S in the word MISSISSIPPI, we need to consider the positions of the remaining 10 letters (M, I, S, S, I, S, S, I, P, P).
Since we're fixing the positions of the first and last letters, we are left with 8 positions to fill with the remaining letters. We can think of this as arranging 8 objects in these 8 positions.
To find the number of permutations, we can use the formula for permutations of n objects taken r at a time, which is given by nPr = n! / (n-r)!. In this case, n = 8 and r = 8, so the number of permutations is:
8P8 = 8! / (8-8)! = 8! / 0! = 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Therefore, there are 40,320 permutations that begin with P and end with S in the word MISSISSIPPI.