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Question
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Solution
In this problem first, we have to select consonants and vowels.
Then we arrange a five-letter word using 3 consonants and 2 vowels.
Therefore here both combination and permutation involved.
The number of ways of selecting 3 consonants from 7 is 7C3.
The number of ways of selecting 2 vowels from 4 is 4C3.
The number of ways selecting 3 consonants from 7 and 2 vowels from 4 is 7C3 × 4C2.
Now with every selection number of ways of arranging 5 letter word
= 5! × 7C3 × 4C2
= 120 ×`(7 xx 6 xx 5)/(3xx2xx1) xx (4xx3)/(2xx1)`
= 25200
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