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)
=` (7_(C _ 3) xx 4_(C _ 2))`
= `((7 xx 6 xx 5)/(3 xx 2 xx 1) xx (4 xx 3)/(2 xx 1))` = 210
Number of groups , each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters
Number of ways of arranging 5 letter among themselves.
= 5 ! = ( 5 x 4 x 3 x 2 x 1) = 120.
`:.` Required number of words = (210 x 120) = 25200.
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