What are the number of such words formed

Out of 7 consonants and 4 vowels,words are to be formed by involving 3 consonants and 2 vowels. The number of such words formed is :

  1. -25200
  2. 22500
  3. 10080
  4. 5040
Anurag Mishra Professor Asked on 17th March 2016 in Reasoning Questions.
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1 Answer(s)

Answer: (1) 25200

Solution:-

Number of ways of selecting 3 consonants out of 7 = 7C3
Number of ways of selecting 2 vowels out of 4 = 4C2
Number of ways of selecting 3 consonants out of 7 and 2 vowels out of 4 = 7C3 x 4C2
=(7×6×5/3×2×1)×(4×32×1)=210
It means that we can have 210 groups where each group contains total 5 letters   (3 consonants
and 2 vowels).

Number of ways of arranging 5 letters among themselves = 5!
= 5 x 4 x 3 x 2 x 1 = 120

Then, Required number of ways = 210 x 120 = 25200

Hence, the correct answer is option (1) 25200.

Anurag Mishra Professor Answered on 18th March 2016.
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