Question

Seven students are competing in a race. In how many different combinations could the seven students place in the race?

Answer 1

There are 7 students competing in the race.

To find the number of different combinations in which they could place in the race, we can use the formula for combinations:

C(n, k) = n! / (k!(n-k)!)

where n is the total number of students (7) and k is the number of students in each combination (1st, 2nd, 3rd, etc.).

For the first place, there are 7 students who could come in first. For the second place, there are 6 students who could come in second, and so on.

So, the total number of different combinations in which the seven students could place in the race is:

C(7, 1) * C(6, 1) * C(5, 1) * C(4, 1) * C(3, 1) * C(2, 1) * C(1, 1) = 7! = 5040

There are 5040 different combinations in which the seven students could place in the race.