How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

Options

A. `""^(5)C_(2)xx""^(17)C_(3)`
B. `""^(5)C_(2)xx5!`
C. `""^(17)C_(3)xx5!`
D. `""^(5)C_(2)xx""^(17)C_(3)xx5!`

Answer

D

Explanation

There are 5 vowels and 17 consonants. Two vowels out of 5 vowels and 3 consonants out of 17 consonants can be chosen in `""^(5)C_(2)xx""^(17)C_(3)` ways. Now, we have 5 letters which can be arranged in 5! ways .
Total number of words `""^(5)C_(2)xx""^(17)C_(3)xx5!`