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gmatter2012
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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?
No. of vowels - 3As, 1U, 1Igmatter2012 wrote: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?
No. of consonants - 1S, 1T, 1R, 1L
Two vowels and two consonants need to be chosen at a time.
1) CASE-1 If those two vowels are same i.e., 2As and two different consonants are chosen in 4C2 (6 ways).
No. of permutations for those two chosen consonants and vowels for a 4 letter word - 4!/2! = 12 ways
As we can choose the consonants in 6 ways, total no. of different words = 72
2) CASE-2: Both vowels are different and both consonants are different.
We can choose 2 different vowels in 3 ways (A,U), (U,I), (A,I)
We can choose 2 different consonants in 4C2 ways = 6 ways
To form a 4 letter word, (for any 2 selected vowels and any 2 selected consonants) No. of permutations will be = 4! = 24 ways.
Total no. of 4 letter words = 6*3*24 = 432
Adding the two case, Total no. of 4 letter words = 432+72= 504
Kindly write the OA. I am not very sure about my approach here
