Question

A 9 passenger van shuttles athletes between venues at the canada summer games. If 22 athletes need to get to the track and field stadium, in how many ways can passengers be chosen for
A) the bus’s first trip?

Combinations

Answer 1

To determine the number of ways passengers can be chosen for the first trip, we need to find the number of combinations of 22 athletes taken 9 at a time. This can be calculated using the formula for combinations:

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

where C(n, r) represents the number of combinations of n objects taken r at a time.

In this case, n = 22 (number of athletes) and r = 9 (number of seats in the van).

C(22, 9) = 22! / (9!(22-9)!) = 22! / (9!13!) = (22 * 21 * 20 * 19 * 18 * 17 * 16 * 15 * 14) / (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying the expression:

C(22, 9) = 2,027,025 / 362,880

Thus, there are 2,027,025 ways passengers can be chosen for the bus's first trip.