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Question: Number of ways in which 12 different things can be distributed in 5 sets of 2, 2, 2, 3, 3 things is...

Number of ways in which 12 different things can be distributed in 5 sets of 2, 2, 2, 3, 3 things is

A

12!(3!)2(2!)3\frac{12!}{(3!)^{2}(2!)^{3}}

B

12!5!(3!)2(2!)3\frac{12!5!}{(3!)^{2}(2!)^{3}}

C

12!(3!)3(2!)4\frac{12!}{(3!)^{3}(2!)^{4}}

D

12!5!(3!)2(2!)4\frac{12!5!}{(3!)^{2}(2!)^{4}}

Answer

12!(3!)3(2!)4\frac{12!}{(3!)^{3}(2!)^{4}}

Explanation

Solution

Required ways = 12C3x9C3x6C2x4C2x2C23! 6mu2!\frac{12C_{3}x^{9}C_{3}x^{6}C_{2}x^{4}C_{2}x^{2}C_{2}}{3!\mspace{6mu} 2!}

= 12!9!3!x9!6!3!x6!4!2!x4!2!2!x13!2!\frac{12!}{9!3!}x\frac{9!}{6!3!}x\frac{6!}{4!2!}x\frac{4!}{2!2!}x\frac{1}{3!2!} = 12!(3!)3(2!)4\frac{12!}{(3!)^{3}(2!)^{4}}