In how many different ways can a chairperson and a secretary be selected from a committee … — JAMB UTME

In how many different ways can a chairperson and a secretary be selected from a committee of $5$ members?

The number of ways to select a chairperson and a secretary from

5

members is

20

Selecting

2

individuals for distinct positions (chairperson and secretary) from

5

candidates is an ordered selection problem. The number of ways is given by the permutation formula

_5P_2 = 5 \times 4 = 20

Identify whether order matters

Order matters because the roles of chairperson and secretary are distinct.

When distinct roles are assigned, the arrangement is a permutation rather than a combination.

Apply the permutation formula

_nP_r = \frac{n!}{(n-r)!}

for

n=5

and

r=2

_5P_2 = \frac{5!}{(5-2)!} = \frac{5!}{3!} = 5 \times 4 = 20

There are

5

choices for chairperson and

4

remaining choices for secretary.

Permutation of

n

distinct items taken

r

at a time

Estimated Time:45s

Question