Question

The number of $4$ letter words containing equal number of vowels and consonants, where repetition is allowed, is

• A. ${105}^2$
• B. $210\times 243$
• C. $105\times 243$
• D. $150\times {21}^2$

Answer 1

The correct option is D $150\times {21}^2$

Here, repetition is allowed
We will be having $2$ vowels and $2$ consonants
Selecting two places for vowels can be done by ${}^4{C}_2$ ways.
Now this places can be filled by vowels in $5\times 5$ ways.
The remaining places can be filled by consonants in $21\times 21$ ways
$\therefore$ Total ways are ${}^4{C}_2\times 5\times 5\times 21\times 21=150\times {21}^2$