Question

Let $E$ denote the set of letters of the English alphabet, $V=\{a,e,i,o,u\}$, and $C$ be the complement of $V$ in $E$. Then, the number of four-letter words (where repetitions of letters are allowed) having at least one letter from $V$ and at least one letter from $C$ is

• A. $261870$
• B. $314160$
• C. $425880$
• D. $851760$

Answer 1

The correct option is A $261870$

$V$ is the set of vowels then,
$C$ will be the set of consonants.
Number of 4 letters word with only vowels $=5^4$
Number of 4 letters word with only consonants $=(21{)}^4$
Total words $=(26{)}^4$
Required number of words
$=(26{)}^4-(21{)}^4-(5{)}^4=261870$