COLLEGE MATH!!!!!!!

Question

In how many ways can the letters in the word A P P L E S A U C E be arranged?

Answer 1

sorting the 10 letters: A A C E E L P P S U

10!/ (2! 1! 2! 1! 2! 1! 1!) <--- each letter's frequency appears in the denominator

10! / (2*2*2) <--- 1! = 1 which gets multiplied out; 2! = 2

10! / 8

= 10 * 9 * 7*6*5*4*3*2*1 <--- 8 cancels

=453600