Question

In how many ways can the letter of the word $DELHI$ be arranged, so that the vowels occupy only the even places?

• A. $2$
• B. $6$
• C. $12$
• D. $36$

Answer 1

The correct option is C $12$

Given: The number of letters in the word DELHI = 5

we know that the number of vowels in the given word DELHI are E,I = 2

And the number of even places which these vowels can occupy are 2 (second and fourth)

Thus the number of ways to arrange vowels in the even places $={{}^{2}P}_2$

And the number of ways to arrange the remaining 3 letters in 3 places $={{}^{3}P}_3$

So the total number of ways $={{}^{2}P}_2\times {{}^{3}P}_3=12$