Question

The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.

Options

• 96

• 144

• 512

• 576

Answer 1

The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is 576.

Explanation:

The vowels in the word ‘COMBINE’ are O, I and E which can be arranged at 4 places in ⁴P₃ ways and other words can be arranged in 4! ways.

Hence, the total number of ways = ⁴P₃ × 4!

= 4! × 4!

= 576