Question

out of 7 consonants and 4 vowels,how many words of 3 consonants and 2 vowels can be formed?
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Answer 1

GIVEN :-

• No. of consonants = 7
• No. of vowels = 4

TO FIND :-

• No. of consonants and vowels formed respectively 3 and 2

SOLUTION :-

• We should choose 3 consonants and 2 vowels from 7 consonant and 4 vowels

Required Combination-

$\sf 7C_{ 3} \: \times 4C_{ 2}$

$= \frac{7!}{3!(7 - 3)!} \times \frac{4!}{2!(4 - 2)!}$

$\sf \: Note -$

$\boxed{ \green{ \sf nC_{ r} = \frac{n!}{r!(n -r) !} } }$

$= \frac{7!}{3!(4)!} \times \frac{4!}{2!(2)!}$

$= \frac{7 \times 6 \times 5 \times \cancel{4!}}{3!( \cancel{4)!}} \times \frac{4 \times 3 \times \cancel{2!}}{2!( \cancel{2)!}}$

$= \frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{4 \times 3}{2 \times 1}$

$= 35 \times 6$

$\sf = 210$

• Total 210 words be formed.