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 7 Pocks. 6 Taup. 2 Kares. and 4 Vokut and suppose that a 4-member subcommittee is formed for the purpose of studying the emotional response to new technologies in older adults. How many different subcommittees arc possible? How many different subcommittees consist of at least 1 Taup? How many different subcommittees consist of exactly 2 Pocks and 1 Vokut?

Explanation / Answer

(a) 4 members can be chosen from the total of 7+6+2+4 = 19 as 19C4 = (19X18X17X16)/(1X2X3X4) = 93024/24 = 3876

(b) Number of subccommittees with at least 1 Taup = 1 - Number of subcommittees with no Taup.

Number of subcommittees with no taup = 13C4 = (13X12X11X10)/(1X2X3X4) = 17160/24 = 715

So, Number of subcommittees with at least 1 Taub = 3876-715 = 3101

(c) 2 Packs can be chosen from 7 packs = 7C2 = (7X6)/(1X2) = 21

1 Vokut can be chosen from 4 Vokut = 4

Remaining 1 can be chosen from 8 = 8

So, number of ways= 21X4X8=672

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