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Question

Find the number of seven lettered words each consisting of three vowels and four consonants which can be formed using the letters of the word DIFFERENTIATION.

A
432551
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B
325710
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C
252000
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D
644004
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Solution

The correct option is B 325710
DIFFERENTIATION
Vowels - I,E,E,I,A,I,O
Consonants - D,F,F,R,N,N,T,T
No of ways of selecting :
3 vowels
All different =4C3=4 2 same, 1 different=2C1 3C2=63 same=1

4 consonants
All different=5C4=52 same, 2 different=3C1×4C2=182 pair same=3C2=3

Required number of ways
=4×5×7!+4×18×7!2!+4×3×7!2!2!+6×5×7!2!+6×18×7!2!2!+6×3×7!2!2!2!+1×5×7!3!+1×18×7!3!2!+1×3×7!2!2!3!=325710

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