Question

2.) What is the total number of different seven-letter arrangements that can be formed using the letters in the word "MILLION"? * O 1) 30 O 2) 210 3) 1,260 4) 2,520

Answer 1

ANSWER

3) 1260

EXPLANATION

We want to find the total number of different seven letter arrangements that can be made out of MILLION.

First, we know that MILLION has 7 letters.

We don't want a case of repeated letters, because we want 7 different letter arrangements.

There are 2 repeated letters there, I and L, therefore, our answer will be:

$\frac{7!}{2!\text{ 2!}}\text{ = }\frac{5040}{2\cdot\text{ 2}}\text{ = 1260}$

There are 1260 ways to arrange it.