Question

Using the letters of the word,’ ARRANGEMENT’ how many different words (using all letters at a time) can be made such that both A, both E, both R and both M occur together.

Answer 1

There are 11 letters in the word ‘ARRANGEMENT’ out of which 2A’s, 2E’s, 2R’s and 2M’s. 

Considering both A, both E, both R and both M together, 8 letters should be counted as 4. 

So, there are total 7 letters (AA EE RR MM G M T) 

These 7 letters can be arranged in 7! Ways 

Hence, total ways = 7! 

= 7 × 6 × 5 × 4 × 3 × 2 × 1 

= 5040