Out of 8 consonants and 3 vowels, how many words of 3 consonants and 2 vowels can be formed?

Question: Out of 8 consonants and 3 vowels, how many words of 3 consonants and 2 vowels can be formed?

Solution:
Number of ways of selecting (3 consonants out of 8) and (2 vowels out of 3)
= (⁸C₃ × ³C₂) = 56 × 3 = 168


Number of groups, each having 3 consonants and 2 vowels = 168
Each group contains 5 letters.
Number of ways of arranging
5 letters among themselves
= 5!
= 5 × 4 × 3 × 2 × 1
= 120.
Required number of ways = (168 × 120) = 20160