Question

The probability that in a random arrangement of the letters of the word 'ANIMAL', the two A's come together.

• A. 4/5
• B. 2/5
• C. 2/3
• D. 1/3
• E. none

Answer 1

The correct option is D

1/3

The total number of words which can be formed by permuting the letters of the word 'ANIMAL' is $\frac{6!}{2!}$ as there are two A's.

Hence n(S)=$\frac{6!}{2!}$

Taking two A's as one letter, the number of ways of arrangement in which both A's are together = 5!
So n(X)=5!

Hence required probability=$\frac{n\left(X\right)}{n\left(S\right)}$=$\frac{1}{3}$