Practice!

Sample Problem

In how many ways can the letters of the word MISSISSIPPI be rearranged to form a new (11-letter) “word?”

 

Solution

Notice that in the word Mississippi, we have 4 S’s, 2 P’s, and 4 I’s, all of which create the possibility of overcounting. Therefore, we will first find the number of ways in which we can arrange the letters if all the letters were different, which is

11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 11!

Then, we divide this number by the number of ways to overcount each letter.

Thus, for the S’s, we divide by 4 × 3 × 2 × 1 = 24.

For the I’s, we do the same: Divide by 24.

For the P’s, we divide by 2 × 1 = 2.

Therefore, our final answer is

  = 34650.