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Question: The number of words of four letters containing equal number of vowels and consonants, repetition bei...

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

A

1052

B

210 × 243

C

105× 243

D

None

Answer

210 × 243

Explanation

Solution

The number of selections of 1 pair of vowels and 1 pair of consonants = 5C1 × 21C1

The number of selections of 2 different vowels and 2 different consonants = 5C2 × 21C2

∴ The required number of words

= 5C1 × 21C1 × 4!2!2!\frac{4!}{2!2!} + 5C2 × 21C2 × 4!