Question

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

Answer 1

Answer:

151200

Step-by-step 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 $\frac{n!}{n1!n2!...nk!}$ , with n representing the amount of letters and each subset of n representing the amount of each letters, our answer is

$\frac{10!}{3!2!2!1!1!1!} = \frac{10!}{3!2!2!} = 151200$