Question

In: Statistics and Probability

After the 400m race at the Olympics, which has 8 participants, the champions of the Gold,...

After the 400m race at the Olympics, which has 8 participants, the champions of the Gold, Silver and Bronze medals stand together on a tiered plinth, with Gold on the highest level, etc. A picture is then taken of the three of them. If a picture is only considered unique if the athletes are not in the same positions (i.e., a slightly different picture of the same people in the same position is not unique), then how many unique pictures of the athletes are there?

Solutions

Expert Solution

A picture is only considered unique if the athletes are not in the same positions.

This implies that there are different athletes in the champions of the Gold position, the champions of the Silver position and champions of the Bronze position; in each unique picture.

Thus; number of unique pictures of the athletes that are there

= Number of permutations of the champions of the Gold, Silver and Bronze medals that are possible from 8 athletes

The champion of the Gold medal can be any of the 8 athletes.

The champion of the Silver medal can be any of the remaining 7 athletes.

The champion of the Bronze medal can be any of the remaining 6 athletes.

Thus, number of permutations of the champions of the Gold, Silver and Bronze medals that are possible from 8 athletes = 876 = 336

Thus; number of unique pictures of the athletes that are there = 336

orchestra answered 2 years ago
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