## Task 4 - 030524

Klaus, Ingrid, Peter, and Susanne are supposed to participate in a relay race at a sports festival.

a) How many different possibilities are there for the order in which they run? Justify your answer!

b) How many possibilities would there be if the relay consisted of five runners?
a) First, Klaus, Ingrid, Peter, or Susanne can stand in the first place. This gives 4 possibilities.

If one child is selected, there are still 3 children who can stand in the second place, which means 3 possibilities. The remaining 2 children can take the last two places, and there are 2 possibilities for this.

In total, this results in $4 \cdot 3 \cdot 2 = 24$ different sequences.

b) For each sequence of the four students from part a), the fifth student can be placed before the first, before the second, before the third, before the fourth, or at the end. This gives 5 possibilities.

Thus, the result is five times the result from part a), which is 120.