The number of 4-letter words, with or without | vedclass

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(D) The word $INCONSEQUENTIAL$ consists of $15$ letters. First, identify the distinct vowels and consonants. Vowels: {$I$, $O$, $E$, $U$, $A$} ($5$ di

Vedclass · Accepted Answer

$3600$

Vedclass · Answer

(D) The word $INCONSEQUENTIAL$ consists of $15$ letters. First, identify the distinct vowels and consonants. Vowels: {$I$, $O$, $E$, $U$, $A$} ($5$ distinct vowels). Consonants: {$N$, $C$, $S$, $Q$, $T$, $L$} ($6$ distinct consonants). We need to select $2$ vowels out of $5$ and $2$ consonants out of $6$. The number of ways to choose these letters is $\binom{5}{2} 	imes \binom{6}{2} = 10 	imes 15 = 150$. Each selection contains $4$ distinct letters, which can be arranged in $4! = 24$ ways. Total number of words = $150 	imes 24 = 3600$.

The number of $4$-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word $INCONSEQUENTIAL$, without repeating any letter, is:

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