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Question
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
Options
60
120
7200
720
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Solution
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to 7200.
Explanation:
Given that total numbers of vowels = 4
And total numbers of consonants = 5
Total number of words formed by 2 vowels and 3 consonants
= 4C2 × 5C3
= `(4!)/(2!2!) xx (5!)/(3!2!)`
= `(4 xx 3 xx 2!)/(2 xx 1 xx 2!) xx (5 xx 4 xx 3!)/(3! xx 2)`
= 6 × 10
= 60
Now permutation of 2 vowels and 3 consonants = 5!
= 5 × 4 × 3 × 2 × 1
= 120
So, the total number of words = 60 × 120 = 7200.
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