The 50m Race: Solution

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Andrew, Beth, Hanga, and Ieri were the only runners in their school’s 50m race. In how many possible ways could they finish if Hanga came first?

Solution

The easiest way to solve this is to make a list. If we know that Hanga came first then Andrew, Beth or Ieri must have come second. Then one of the others must have come third, and the last one fourth. If you make a complete list you should find 6 answers.

Hanga, Andrew, Beth, Ieri

Hanga, Andrew, Ieri, Beth

Hanga, Beth, Andrew, Ieri

Hanga, Beth, Ieri, Andrew

Hanga, Ieri, Andrew, Beth

Hanga, Ieri, Beth, Andrew

The answer is 6.

Extension

How many ways could the four runners finish if anyone could come first?