Question

a. Eight runners are entered in a race where there are only prizes for a first,...

a. Eight runners are entered in a race where there are only prizes for a first, second or third place finish. How many ways can eight runners be arranged into first, second, third?

b.From a class of 50 students , a committee of 5 students is needed to manage the annual BBQ. How many ways can the committee of 5 be chosen?

Math   Statistics-And-Probability   
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Answer #1

Part A:

The order in which the runners finish matters, so this is a permutation rather than a combination.

Until the first runner crosses the finish line, there are eight runners who could finish first.

Once the first runner crosses the finish line, there are seven runners who could finish second.

Once the first two runners have crossed the finish line, there are six runners who could finish third, giving

8 * 7 * 6 = 336

So, there are 336 ways.

Part B:

Number of students in a class = 50

We are choosing 5 members in a committee.

So, we need to use combination.

It should be 50C5.

Hence, number of ways to choose 5 = 2118760

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