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

Question

The global government of the planet Clavnu functions as a democracy with four major political parties, the Pocks, the Taup, the Kares, and the Vokut. The technology education committee of the government currently consists of 9 Pocks, 3 Taup, 5 Kares, and 4 Vokut and suppose that a 4-member subcommittee is formed for the purpose of study 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 Vokut?

c) How many different subcommittees consist of exactly 1 Taup and 2 Pocks?

Explanation / Answer

There are 21 people to choose from.

a)

There are 21C4 = 5985 ways [ANSWER]

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b)

There are 4 ways to choose a Vokut.

Now, there are 20C3 = 1140 ways to choose the other 3.

Hence, all in all

1140*4 = 4560 ways [ANSWER, at least 1 Vokut]

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c)

There are 3 ways to choose 1 Taup.

There are 9C2 = 36 ways to choose 2 Pocks.

Now, there are 5+4 = 9 ways to choose the last one in Kares and Vokut.

Hence, a total of

3*36*9 = 972 ways [ANSWER]

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