Question

Out of $7$ consonants and $4$ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2$ vowels, is

• A. 24800
• B. 25100
• C. 25200
• D. 25400

Answer 1

Answer: (C)

$3$ consonants can be selected from 7 consonants$={}^7{C}_3\text{ ways }$
$2$ vowels can be selected from 4 vowels
$={}^4{C}_2\text{ ways }$
$\therefore$ Required number of words
$={}^7{C}_3\times {}^4{C}_2\times 5!$
[selected $5$ letters can be arrange in $5!$, so get, a different words]
$=35\times 6\times 120=25200$