Question

How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels?

• A. ${}^5{C}_3{\times }^4{C}_2$
• B. $\frac{{}^5{C}_3{\times }^4{C}_2}{5}$
• C. ${}^5{C}_3{\times }^4{C}_3$
• D. $\left({}^5{C}_3{\times }^4{C}_2\right)\left(5!\right)$

Answer 1

Answer: (D)

$\left({}^5{C}_3{\times }^4{C}_2\right)\left(5!\right)$

No .of consonant $5$

NO .of Vowels $4$

No. of consonants required $3$

No.of Vowels Required $2$

Selecting Consonants ${}^5{C}_3$

Selecting Vowels ${}^4{C}_2$

Total no .of Selections ${}^5{C}_3{\times }^4{C}_2$

No. of arrangements $5!$

Total number of words ${}^5{C}_3{\times }^4{C}_2\times 5!$