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

A four letter word containing equal number of vowels and consonants may contain one vowel and one consonant or two vowels and two consonants. The number of four letter words containing one vowel and one consonant

${=}^5{C}_1{\times }^{21}{C}_1\times \frac{4!}{2!2!}$

The number of four letter words containing two vowels and two consonants ${=}^5{C}_2{\times }^{21}{C}_2\times 4!$

Hence, required number of words

$\begin{array}{l}{=}^5{C}_1{\times }^{21}{C}_1\times \frac{4!}{2!2!}{+}^5{C}_2{\times }^{21}{C}_2\times 4!\\ =105\times 6+10\times 210\times 24=210(3+240)=210\times 243\end{array}$