Question

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

Answer 1

Total number of ways of choosing (3 consonants out of 7) and (2 vowels out of 4)

= ${(}^7{C}_3{\times }^4{C}_2)=(\frac{7\times 6\times 5}{3\times 2\times 1}\times \frac{4\times 3}{2\times 1})=210.$

Number of groups, each containing 3 consonants and 2 vowels = 210.

Each group contains 5 letters.

Number of ways of arranging 5 letters amongst themselves

= $5!=(5\times 4\times 3\times 2\times 1)=120.$

Hence, the requried number of words = $(210\times 120)=25200.$