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: [2026]

Question

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: [2026]

Smart Achievers · Accepted Answer

(4)

In word INCONSEQUENTIAL, distinct vowels are (I, E, O, A, U) and distinct consonants are (N, C, S, Q, T, L)

Total number of 4 letter words using two vowels and two consonants without repetition = ${}^{5}C_{2} \times {}^{6}C_{2} \times 4!$ = 3600

Solution

Q.
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: [2026]

1 2670

2 2840

3 2920

4 3600

Ans.
(4)

In word INCONSEQUENTIAL, distinct vowels are (I, E, O, A, U) and distinct consonants are (N, C, S, Q, T, L)

Total number of 4 letter words using two vowels and two consonants without repetition = ${}^{5}C_{2} \times {}^{6}C_{2} \times 4!$ = 3600

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