JEE Main 2026 — Permutation Combination Question with Solution

The given word is INCONSEQUENTIAL.

The vowels present in the word are I, O, E, U, A. There are $5$ distinct vowels.

The consonants present in the word are N, C, S, Q, T, L. There are $6$ distinct consonants.

We need to form $4$-letter words consisting of $2$ vowels and $2$ consonants without repeating any letter. This means all $4$ letters in the formed word must be distinct.

Number of ways to select $2$ distinct vowels from $5$ distinct vowels = ${}^5{C}_2=\frac{5\times 4}{2}=10$

Number of ways to select $2$ distinct consonants from $6$ distinct consonants = ${}^6{C}_2=\frac{6\times 5}{2}=15$

Number of ways to arrange the $4$ selected letters = $4!=24$

Total number of $4$-letter words that can be formed = $10\times 15\times 24=3600$

Answer: $3600$