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?
B) the bus’s second trip?
A) For the bus's first trip, since there are 22 athletes who need to go to the track and field stadium, there are 22 athletes to choose from. Therefore, there are 22 ways to choose the passengers for the bus's first trip.
B) Once the athletes from the first trip have arrived at the track and field stadium, they are no longer available for the second trip. So, for the bus's second trip, there are 22 - 9 = 13 athletes remaining who still need to get to the track and field stadium. Therefore, there are 13 ways to choose the passengers for the bus's second trip.
A) For the bus's first trip, we need to choose 9 passengers out of 22 athletes. This can be calculated using the combination formula "nCr", where n is the total number of athletes and r is the number of passengers we want to choose. In this case, n = 22 and r = 9.
The formula for combination is: nCr = n! / (r!(n-r)!)
Plugging in the values, we get:
22C9 = 22! / (9!(22-9)!) = (22 * 21 * 20 * 19 * 18 * 17 * 16 * 15 * 14) / (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= 685464120 / 362880
= 189924
Therefore, there are 189,924 ways to choose passengers for the bus's first trip.
B) For the bus's second trip, we need to choose 9 passengers out of the remaining 13 athletes (since 22 - 9 = 13). Using the same combination formula:
13C9 = 13! / (9!(13-9)!) = (13 * 12 * 11 * 10) / (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= 1716 / 362880
= 4
Therefore, there are 4 ways to choose passengers for the bus's second trip.