There are

6
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?

30

How many different riders could come in first ? 6

That leaves how many to come in second? 5

what is 6x5 ??

How many cyclists can get first. 6 of them can get first. For every single cyclist 5 others can get second. You then multiply 6 and 5.

If third place was added you would also multiply 6 and 5 with 4 to get that answer.

6 cyclists 2 prizes ?

To find the number of different ways the prizes can be awarded, we can use the concept of permutations.

In this case, there are 6 cyclists in the race, and we need to award prizes to 2 of them. The first prize can be awarded to any of the 6 cyclists, and once that is done, the second prize can be awarded to any of the remaining 5 cyclists.

Therefore, we can calculate the number of ways the prizes can be awarded by multiplying the number of choices for the first prize by the number of choices for the second prize:

Number of ways = 6 * 5 = 30

So, there are 30 different ways the prizes can be awarded in this race.