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Question 1:
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A. 24400
B. 21300
C. 210
Feedback Number of ways of selecting 3 consonants from 7= 7C3
Number of ways of selecting 2 vowels from 4= 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 × 4C2
=(7×6×5/3×2×1)×(4×3/2×1)=210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves=5!=5×4×3×2×1=120
Hence, required number of ways=210×120=25200
D. 25200
Feedback Number of ways of selecting 3 consonants from 7= 7C3
Number of ways of selecting 2 vowels from 4= 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 × 4C2
=(7×6×5/3×2×1)×(4×3/2×1)=210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves=5!=5×4×3×2×1=120
Hence, required number of ways=210×120=25200

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