SOLUTION: 1. Find the number of distinguishable permutations of the letters of the word PROPOSAL.

There are 8 letters, which, if distinct, would give 8! permutations.



Since there are 2 O's, 2 P's, we need to divide by 2!*2! as the permutations of those identical letters are indistinguishable:



8!/(2!*2!) = 10080