How many different strings can be made from the word PEPPERC

How many different strings can be made from the word PEPPERCORN when at least 9 of the letters are used? (SHOW WORK & Explaination)

Solution

We have 10 letters (in the word PEPPERCORN) that can be permuted in 10! ways but because some of the letters repeat themselves
we counted some of the arrangements more than once. So the actual number of dictinct ways to
arrange the letters is 10!/ (3!*2!*2!) = 10!/24 => 3628800/24 => 151200 ( we have 3 P’s which were counted 3! Times , 2 E’s
permuted again 2! Times and 2 R’s permuted again 2! Times)