The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is

Question

The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is (A) 1052 (B) 210 × 243 (C) 105 × 243 (D) 150 × 212

Tardigrade Admin · Accepted Answer

Let us first select two places for vowel, which can be selected from 4 places in 4C2 ways. Now this places can be filled by vowels in 5 × 5 = 25 ways as repetition is allowed. The remaining two places can be filled by consonants in 21 × 21 ways. Then the total number of words is 4C2 × 25 × 212 = 150 × 212.

Q. The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is

$10 5^{2}$

$210 \times 243$

$105 \times 243$

$150 \times 2 1^{2}$

Q. The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is

1052

210×243

105×243

150×212

$10 5^{2}$

$210 \times 243$

$105 \times 243$

$150 \times 2 1^{2}$