Suppose that an education committee of the government currently consists of 9 De

Question

Suppose that an education committee of the government currently consists of 9 Democrats, 5 Replucblicans, and 2 Independents and suppose that a 3-member subcommittee is formed for the purpose of study the difficulty of learning about inorganic chemistry in an online environment.

a) How many different subcommittees are possible?

b) How many different subcommittees consist of a least 1 Republican?

c) How many different subcommittees consist of exactly 2 democrats and 1 Independent?

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Explanation / Answer

a) Total people = 9 +5 +2 = 16

No. of subcommittees formed = 16C3 = 16!/3!13! = 560

b) Atleast Republican:

1 republican : 5C1*11C2

2 republican : 5C2*10C1

3 republican : 5C3

So, no. of different subcommittees consist of a least 1 Republican = 5C1*11C2 +5C2*10C1+ 5C3

= 5*55 +10*10 + 10

= 385

c) different subcommittees consist of exactly 2 democrats and 1 Independent

9C2*2C1 = 36*2 = 72

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