There are
5
cyclists in a race. There will be a first-place and a second-place prize awarded. In how many different ways can the
2
prizes be awarded?
5P2 = ?
You have to answer
3
essay questions for an exam. There are
6
essays to choose from. How many different groups of
3
essays could you possibly choose?
To find out how many different ways the prizes can be awarded, we can use the concept of permutations.
In this case, we have 5 cyclists and 2 prizes to be awarded - first-place and second-place.
The number of ways the first-place prize can be awarded is equal to the number of options (5 cyclists) because any of the 5 cyclists can win the first prize.
Once the first-place prize is awarded, we are left with 4 cyclists for the second-place prize. Therefore, the number of ways the second-place prize can be awarded is equal to the number of options (4 cyclists).
To find the total number of ways the prizes can be awarded, we multiply the number of ways the first-place prize can be awarded by the number of ways the second-place prize can be awarded. Using the multiplication principle, we get:
Number of ways = 5 (for the first-place prize) * 4 (for the second-place prize) = 20.
Therefore, there are 20 different ways the prizes can be awarded in this race.