Question

The number of permutations by taking all letters and keeping the vowels of the word 'COMBINE' in odd places is equal to:

• A. $96$
• B. $144$
• C. $512$
• D. $576$

Answer 1

The correct option is D

$576$

Explanation for the correct option:

Find the required number of permutations.

In the question, the word ‘$COMBINE$’ is given.

There are three vowels $E,I,O$ and four odd places.

So, the number of ways in which these three vowels can be arranged is ${}^{4}P_3=24$.

And the number of ways in which remaining letters can be arranged is ${}^{4}P_3=24$.

So, the total number of permutations is $24·24=576$.

Therefore, the number of permutations by taking all letters and keeping the vowels of the word '$COMBINE$' in odd places is equal to $576$.

Hence, option $D$ is the correct option.