Question

In how many different ways can the letters of the word 'RETAIL' be arranged in such a way that the vowels occupy only the odd positions?

• A. 16
• B. 26
• C. 36
• D. 46

Answer 1

The correct option is C 36

The word 'RETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)
The 3 vowels(EAI) must occupy only the odd positions. Let's mark the positions as (1) (2) (3) (4) (5) (6).
Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.
Hence, number of ways to arrange these vowels
${=}^3{P}_3=3!=3\times 2\times 1=6=3!=3\times 2\times 1=6$
Now we have 3 consonants(RTL) which can be arranged in the remaining 3 positions in any order. Hence, number of ways to arrange these consonants
${=}^3{P}_3=3!=3\times 2\times 1=6=3!=3\times 2\times 1=6$
Total number of ways = number of ways to arrange the vowels $\times$ number of ways to arrange the consonants $=6\times 6=36$