How many different ways are possible to arrange the letters of the word ldquo CHAIR rdquo so that th...........

Quantitative Aptitude (CDS) Permutation & Combination

How many different ways are possible to arrange the letters of the word “CHAIR” so that the vowels may occupy only the odd positions?

Explanation:

CHAIR has 3 consonants and 2 vowels.
The vowels can be placed in position number 1,3,5.
Therefore, the total number of ways possible
= 3P2 = 3!/1!
= 3×2= 6
For each of these 6 ways the 3 consonants can be occupy the other 3 places in 3P3 ways
= 3!
= 6 ways
Therefore, the Total number of ways
= 6×6
= 36