Question

Out of $7$ consonants and $4$ vowels, how many words of $3$ consonants and $2$ vowels can be formed?

• A. $210$
• B. $1050$
• C. $25200$
• D. $21400$
• E. $Noneofthese$

Answer 1

The correct option is C $25200$

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
$={(}^7{C}_3{\times }^4{C}_2)$
$=\left(\begin{array}{c}\frac{7\times 6\times 5}{3\times 2\times 1}\times \frac{4\times 3}{2\times 1}\end{array}\right)$
$=210$.
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves = 5!
= 5 x 4 x 3 x 2 x 1
= 120.
$\therefore$ Required number of ways = (210 x 120) = 25200.