A committee of 3 members is to be selected from a group of 7 people. In how many different… — JAMB UTME

A committee of $3$ members is to be selected from a group of $7$ people. In how many different ways can this committee be formed?

Answer: 35 ways

Selecting a committee of

3

members from

7

people requires calculating the number of combinations, given by

^7C_3 = \frac{7!}{3!4!} = 35

Identify total elements and group size

n = 7

and

r = 3

Since the arrangement or order of members in the committee does not matter, this is a selection problem (combinations).

Apply the combinations formula

^nC_r = \frac{n!}{r!(n-r)!}

^7C_3 = \frac{7!}{3!4!}

This formula counts the distinct subsets of size

r

that can be chosen from

n

items.

Evaluate the factorial expression

^7C_3 = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35

Expanding

7!

7 \times 6 \times 5 \times 4!

allows cancelling

4!

, leaving

\frac{210}{6} = 35

Combinations formula

^nC_r = \frac{n!}{r!(n-r)!}

Estimated Time:45s

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