Question
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Answer: Option C
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Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= (7C3 x 4C2)
= \(\left(\frac{7\times6\times5}{4\times3\times1}\times\frac{4\times3}{2\times1}\right)\)
= 210.
Number of groups, each having 3 consonants and 2 vowels = 2
Number of ways of arranging
5 letters among themselves = 5!
= 5 x 4 x 3 x 2 x 1
= 120.
So,Required number of ways = (210 x 120) = 25200.
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