Question

Out of seven consonants and four vowels, the number of words of six letters, formed by taking four consonants and two vowels is (Assume that each ordered group of letter is a word):

• A. $210$
• B. $462$
• C. $1512004$
• D. $332640$

Answer 1

Answer: (C)

$1512004$

Number of selections of $4$ consonants out of $7$ is${}^7{C}_4$

Number of selections of $2$ vowels from $4$ is ${}^4{C}_2$

A word of $6$ letters is to be formed.

Therefore arrangement of words is in $6!$ ways

Hence desired words ${=}^7{C}_4\times {}^4{C}_2\times 6!=151200$