Permutation and Combination - Arithmetic Aptitude Questions and Answers

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Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

210

1050

25200

21400

None of these

Answer : Option A

Explanation :

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)= (⁷C₃ x ⁴C₂)

= [\( \frac { 7*6*5 } {3*2*1 } \)x \( \frac { 4*3 } { 2*1 }\)]

= 210

Number of groups, each having 3 consonants and 2 voweL = 210.

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