A race has 6 competitors. The winner gets a gold ribbon, the second-place finisher gets a blue ribbon, and the third-place finisher gets a red ribbon. In how many ways can the ribbons be awarded?

Question

Mathematics

Reilly Powell

26 May, 03:02

A race has 6 competitors. The winner gets a gold ribbon, the second-place finisher gets a blue ribbon, and the third-place finisher gets a red ribbon. In how many ways can the ribbons be awarded?

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Answers (1)

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Terrence Hines · Answer 1

120 ways

Step-by-step explanation:

Here, we want to calculate the number of ways in which the ribbons can be awarded.

There are 6 competitors and there should only be one first position. What this means is that there are 6 possible ways to become first and 6 possible ways to clinch the gold ribbon.

Now, looking at the second position, since one person already claimed the first, there would be only 5 of the competitors jostling for the second position. This means that the number of ways they can claim the blue ribbon is 5 ways

For the fourth position, there are only 4 competitors wanting to claim the red ribbon. This is because we already have winners for the first and second position.

The number of ways this can be done is thus 4 ways

Now the total number of ways the ribbons can be awarded would be 6 * 5 * 4 = 120 ways