How many ways can first second and third place be awarded to 7 contestants?

So, for example, if we wanted to know how many ways can first, second and third place finishes occur in a race with 7 contestants, there would be seven possibilities for first place, then six choices for second place, then five choices for third place. So, there are 7_∗6_∗5_=210 possible ways to accomplish this.

How many different ways can the first second and third place prizes be awarded?

And for third place? Can’t be the first or second runner but there are 8 others and one of them will be the third. = 720 different possible ways the 3 prizes are awarded.

What made the 8 athletes stop the race?

In David Roth’s poem ‘Nine Gold Medals’, when the youngest athlete stumbled and fell to the ground, the other eight who were ahead of him stopped and came back to help him stand up. That is why all of them were awarded with nine gold medals.

How many runners can be on the first place team?

For first place, you can any one of the 15 runners finish there. For 2nd place, you can have any one of the remaining 14 runners finish there. For 3rd place, you can have any one of the 13 runners who haven’t finished finish there. And for 4th place, you can have any one of the 12 runners who haven’t finished finish there.

How many runners can you pick in a permutation?

This is a classic permutation question. You have 15 runners, and you’re choosing 4 of them, order mattering. So, let’s look at this logically. For first place, you can any one of the 15 runners finish there. For 2nd place, you can have any one of the remaining 14 runners finish there.

How many runners could get second place?

Once we’ve decided that there are ten different first place options, we know that the same runner can’t come in both first and second, so if we ask ourselves how many runners could get second place, there are only nine choices for each combination with a first place winner. In a similar fashion, there are eight possibilities for third place.

How many runners join a race and how many winners?

In the latter case you would take Varun’s calculation and divide by the number of ways 3 winners can be arranged, which is 3*2*1 or 6. And the answer would be 2730 / 6 or 455. Ten runners join a race. How many possible ways can they be arranged as first, second and third places?