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Question: Make a list of all the combinations to find the number of ways of choosing 1 consonant and 2 vowels from the word QUESTION.


A ) 16
B ) 32
C ) 24
D ) 48

Steps to derive

1 Total number of letters in the word 'QUESTION' = 8

2 Vowels in the word 'QUESTION' are U, E, O and I, which are 4 in number.

3 Consonants in the word are Q, S, T and N, which are 4 in number.

4 List all the possible combinations of 2 vowels chosen out of 4 vowels as shown below.
(U, E), (U, I), (U, O)
(E, I), (E, O)
(I, O)

5 There are a total of 6 combinations of choosing 2 vowels.

6 List all the possible combinations of choosing 1 consonant and 2 vowels as follows:
(Q, U, E), (Q, U, I), (Q, U, O), (Q, E, I), (Q, E, O), (Q, I, O)
(S, U, E), (S, U, I), (S, U, O), (S, E, I), (S, E, O), (S, I, O)
(T, U, E), (T, U, I), (T, U, O), (T, E, I), (T, E, O), (T, I, O)
(N, U, E), (N, U, I), (N, U, O), (N, E, I), (N, E, O), (N, I, O)

7 So, 1 consonant and 2 vowels can be chosen in 24 different ways.



Hence the right answer is Option C

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