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
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