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)

25200

Answer 2

$3$ 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]
$=35 \times 6 \times 120=25200$