Question

How many distinct ways can the word EVANESCENCE be arranged if the anagram must end with the letter E?

hint... 10!/2!3!2! = 151,200

Answer 1

151200

Explanation:

We can start by essentially taking off the E at the end, meaning that we want to find all the combinations of

EVANESCENC. We can do this because the combinations will have an E at the end by default.

To solve this, we have to figure out the amount of letters and the amount of each letter. There are 10 letters, with 3 E's, 2 C's, 2 N's, 1 S, 1 V, and 1 A. Using the formula
`(n!)/(n1!n2!...nk!)` , with n representing the amount of letters and each subset of n representing the amount of each letters, our answer is

`(10!)/(3!2!2!1!1!1!) = (10!)/(3!2!2!) = 151200`