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Permutations with Reruns

Let's do another one to make sure you have the idea.

How many ways can we arrange the letters in this word?

M I S S I S S I P P I
 

Let's see...

11 total letters... 11! ... There are 4 I's... 4! ... There are 4 S's... 4! ... There are 2 P's... 2! ... Divide these arrangements out!

 

11! / 4! 4! 2! = ( 11* 10 * 9 * 8 * 7 * 6 * 5 * 4! ) / ( 4! * 4 * 3 * 2 * 1 * 2 * 1 ) ... the 4!'s cancel out ... = ( 11 * 10 * 9 * 8 * 7 * 6 * 5 ) / ( 4 * 3 * 2 * 1 * 2 * 1 ) ... the 8 and the 4 * 2 cancel each other out ... = ( 11 * 10 * 9 * 7 * 6 * 5 ) / ( 3 * 1 * 2 * 1 ) ... the 6 and the 3 * 2 cancel each other out ... = 11* 10 * 9 * 7 * 5 = 34,650

 

YOUR TURN:

How many ways can you arrange the letters in this word?

P O O P E R S C O O P E R