How many ways can the gold, silver, and bronze medals be distributed among the 8 contestants?

In the Olympics, there are 8 swimmers in the final race. How many ways can the gold, silver, and bronze medals be distributed among the 8 contestants?

Solutions

Expert Solution

Step 1

Counting rule: when we selecting elements of a set, then the number of possible outcomes depends on the conditions under which the selection has taken place. there are four types of rules to count the number of possible outcomes:

1) Multiplicative rule

2) Permutation rule

3) Partitions rule

4) Combination rule

Step 2

There are 8 swimmers in the final race. here we want to know that, how many ways can gold, silver, and bronze medals be distributed among 8 contestants.

Therefore, by using the counting rule, there are 8 choices for the gold medal winner, 7 remaining choices for silver, and 6 for the bronze, so there are 8 $\times "> \times$ 7 $\times "> \times$ 6 = 336 ways the three medals can be awarded to the 8 winners.

Raffay answered 2 years ago

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