The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is a. `105^2` b. `210xx243` c. `105xx243` d. `150xx21^2`

Options

A. `105^(2)`
B. `210xx243`
C. `105xx243`
D. none of these

Explanation

A for letter word containing equal number of vowels and consonants may contain one vowel and one consonant of four letter words containing one vowel and one consonant
`=""^(5)C_(1)xx""^(21)C_(1)xx(4!)/(2!2!)`
The number of four letter words containing two vowels and two consonants `=""^(5)C_(1)xx""^(21)C_(2)xx4!`
Hence, required number of words
`=""^(5)C_(1)xx""^(21)C_(1)xx(4!)/(2!2!)+""^(5)C_(2)xx""^(21)C_(2)xx4!` `=105xx6+10xx210xx24=210(3+240)=210xx243`