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JAMB Mathematics 2013 Paper

Question : 29

Total: 47

In how many ways can 3 seats be occupied if 5 people are willing to sit?

Solution:

Concept:

This is a permutation problem because the order in which people occupy the seats matters.

Explanation:

We need to choose and arrange 3 people out of 5.

Number of ways

= {}^5P_3

Using the formula:

{}^5P_3 = \frac{5!}{(5-3)!} = \frac{5!}{2!}

Expand:

\frac{5 \times 4 \times 3 \times 2!}{2!}

Cancel

2!

to get

5 \times 4 \times 3 = 60

So there are 60 possible seating arrangements.

Answer:

A. 60

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