Question

The letters of the word $ARTICLE$ are arranged in all possible ways at random. The probability of arranging them so that the vowels may occupy even places is

• A. $1/2$
• B. $1/6$
• C. $1/8$
• D. $1/4$

Answer 1

The correct option is B $1/6$

Total no of word that can be formed from the letters of the word 'ARTICLE'$=7!$

Total no of even places=3

Total no of vowels=3

Total no of consonants=4

Total no of word having vowels at even places$=3!\times 4!$

So, probability=Word having vowels at even places / Total no of words

$=\frac{3!\times 4!}{7!}$

$=\dfrac{3\times 2\times 1\times 4\times 3\times 2\times 1} {7\times 6\times 5\times 4\times 3\times 2\times 1}$

$=\frac{1}{35}$