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

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

Permutations and Combinations

Solution:

Let us first select two places for vowel, which can be selected from $4$ places in $^4C_2$ ways. Now this places can be filled by vowels in $5 \times 5 = 25$ ways as repetition is allowed. The remaining two places can be filled by consonants in $21 \times 21$ ways. Then the total number of words is $^4C_2 \times 25 \times 21^2 = 150 \times 21^2$.