UPSC NDA Math Model Paper 4

Two letters are chosen from the letters of the word 'EQUATIONS'
Number of sample space = 9C2=

9!

2!7!

=

9×8

2

=36
Vowels in 'EQUATIONS' are E, U, A, I, O and consonants are Q, T, N, S
∴n(one is vowel and the other is consonant) =
5C1×4C1
=5×4
=20
Now, the probability that one is vowel and the other is consonant = 20/36
= 5/9
Hence, option (4) is correct.