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1. Among 30 members of a club, (a) a group of five people is to be selected, in

ID: 3056532 • Letter: 1

Question

1. Among 30 members of a club,

(a) a group of five people is to be selected, in how many ways the selection can happen?

(b) 3 people are to be selected for three different positions (i.e., chair, secretary and accountant). In how many different ways these three positions can be filled?

(c) A picture is going to be taken when 30 people are sitting in two rows of seats. In how many different ways they can sit?

(d) if 5 people are absent from the meeting, in how many ways 25 members can sit on the available 30 seats.

Explanation / Answer

a) Number of ways in which 5 people can be selected from 30 = 30C5

= 30!/(5! x 25!)

= 142,506

b) Number of ways in which 3 positions can be filled = 30P3

= 30!/(30-3)!

= 24,360

c) Number of ways in which 30 people can be seated in 30 seats = 30!

= 2.6525x1032

d) Number of ways in which 25 people can be seated on 30 seats = 30P25

= 2.21x1030