The global government of the planet Arthomid functions as a democracy with four

Question

The global government of the planet Arthomid functions as a democracy with four major political parties,
the Ansidro, the Kwoe, the Maclamarion, and the Troguat. The technology education committee of the
government currently consists of 6 Ansidro, 8 Kwoe, 3 Maclamarion, and 4 Troguat and suppose that a
4-member subcommittee is formed for the purpose of studying the emotional response to new technologies in
older adults.
a) How many different subcommittees are possible?
b) How many different subcommittees consist of at least 1 Kwoe?
c) How many different subcommittees consist of exactly 2 Ansidro and 1 Troguat?

Explanation / Answer

a) There are 6+8+3+4 = 21 members in all and a committe of 4 people can be formed out of them in 21C4 ways

i.e. 5985 ways

b)

In order that committee has no Kwoe , all the 4 members are to be selected from amongst members of the Ansidro, the Maclamarion, and the Troguat, ie. out of 6+3+4 = 13 members and this can be done is 13C4 = 715ways

committee has no Kwoe member = 715

therefore

committee has atleast one kwoe member = 5985- 715= 5270

c) There are 6C2 ways to select 2 Ansidro = 15 ways

There are 4C1 ways to select 1 Troguat = 4

The number of ways to select 1 member for subcommittee from remaining 8+3 =11 members are 11C1 = 11

Total different ways = 15*4*11 = 660

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