Question

The number of ways in which any four letters can be selected from the word "EXAMINATION” if two letters are alike and other two are distinct.

• A. 63
• B. 13
• C. 75
• D. 33

Answer 1

The correct option is A

63

Word "EXAMINATION” has 11 letters out of them there are 3 pairs: {A, A}, {I, I} and {N, N}.

So, number of distinct letters is 8

Two letters are alike and other two are distinct

The number of ways is ${}^3{C}_1{\times }^7{C}_2=63$

${}^3{C}_1$ is a number of ways to choose which two letters will be alike from 3 pairs and ${}^7{C}_2$ is number of ways to choose other two distinct letters from 7 letters which are left.