Question

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Answer 1

In this problem first, we have to select consonants and vowels.

Then we arrange a five-letter word using 3 consonants and 2 vowels.

Therefore here both combination and permutation involved.

The number of ways of selecting 3 consonants from 7 is ⁷C₃.

The number of ways of selecting 2 vowels from 4 is ⁴C₃.

The number of ways selecting 3 consonants from 7 and 2 vowels from 4 is ⁷C₃ × ⁴C₂.

Now with every selection number of ways of arranging 5 letter word

= 5! × ⁷C₃ × ⁴C₂ 

= 120 ×`(7 xx 6 xx 5)/(3xx2xx1) xx (4xx3)/(2xx1)`

= 25200