The five competitors in the final round of a tournament are assured of earning a bronze, silver or gold medal. Any combination of medals is possible, including for example 5 gold medals. How many different combinations of medals can be awarded?

1 Answer
Aviv S.
Jan 27, 2018

The answer is #3^5# or #243# combinations.

Explanation:

If you think of each competitor as a "slot," like this:

_ _ _

You can fill in how many different options each "slot" has. The first competitor may receive a gold, silver, or bronze medal. That is three options, so you fill in the first slot:

3 _ _

The second competitor may also receive a gold, silver, or bronze medal. That is three options again, so you fill in the second slot:

3 3 _ _ _

The pattern continues until you get these "slots":

3 3 3 3 3

Now, you can multiply each of the slot numbers together to get the total number of combinations:

#3*3*3*3*3=3^5=243#

The answer is 243.

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