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There is a word AUSTRALIA. Four letters are taken at random. How many different words can be formed that have two vowels and two consonants?
Vowels: A, U, A, I, A. Distinguish vowles: A, U, I.
Consonants: S, T, R, L
Outcomes with two vowels and two consonants:
1) The two vowels are different: C(3,2)*C(4,2)
2) The two vowels are the same: C(1,1)*C(4,2)
Total outcomes = 18+6=24
I dont understand the 2nd part for two vowels that are the same:2) The two vowels are the same: C(1,1)*C(4,2)