Question

How many words of 4 consonants and 3 vowels can be formed from 6 consonants and 5 vowels

• A. 9979200
• B. 756000
• C. 75600
• D. None of these

Answer 1

The correct option is A 9979200

$4$ constants out of $12$ can be selected in, ${}^{12}{C}_4$ ways

$3$ vowels can be selected in ${}^4{C}_3$ ways

$\therefore$ Total number of groups each containing $4$ consonants and $3$ vowels, $={}^{12}{C}_4\ast {}^4{C}_3$

Each group contains $7$ letters, which can be arranged in $7!$ ways

$\therefore$ Required number of words $={}^{12}{C}_4\ast {}^4{C}_3\ast 7!=9979200$.