Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A. 210
B. 1050
C. 25200
D. 21400
E. None of these
Answer: Option C
Solution(By Examveda Team)
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)$$\eqalign{ & = \left( {{}^7{C_3} \times {}^4{C_2}} \right) \cr & = \left( {\frac{{7 \times 6 \times 5}}{{3 \times 2 \times 1}} \times \frac{{4 \times 3}}{{2 \times 1}}} \right) \cr & = 210 \cr} $$
Number of groups, each having 3 consonants and 2 vowels = 210
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves
= 5!
= 5 x 4 x 3 x 2 x 1
= 120
∴ Required number of ways = (210 x 120) = 25200
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Comments ( 1 )
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
It's correct