First slide

Combinations

Question

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

Moderate

A

105²
B

210 x 243
C

105 x 243
D

150 x 21²

Solution

Let us first select two places for vowel, which can be selected from 4 places in $^{4} C_{2}$ , ways. Now this places can be filled by constants in 21 x 21 ways as repetition is allowed. The remaining two places can be filled by consonants in $^{4} C_{2} \times 25 \times 21^{2} = 150 \times 21^{2}$ .

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