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)

$25200$

$3$ consonants can be selected from $7$ consonants ${=}^7{C}_3$ ways
$2$ vowels can be selected from $4$ vowels ${=}^4{C}_2$ 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]
$=35\times 6\times 120=25200$