Question

Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is ______.

Options

• 24800

• 25100

• 25200

• 25400

Answer 1

Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is 25200.

Explanation:

3 consonants can be selected from 7 consonants = ⁷C₃ ways

2 vowels can be selected from 4 vowels = ⁴C₂ ways

∴ Required number of words = ⁷C₃ × ⁴C₂ x 5!

[selected 5 letters can be arranged in 5! ways, to get a different word]

= 35 × 6 × 120

= 25200