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
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.
To find the number of ways passengers can be chosen for the bus's first trip, we can use the concept of combinations.
In this scenario, we have 22 athletes who need to get to the track and field stadium. Since the van can accommodate 9 passengers, we need to choose 9 athletes out of the 22 for the first trip.
The formula for combinations is given by:
C(n, k) = n! / (k! * (n - k)!)
Where:
- C(n, k) represents the number of combinations of n items taken k at a time.
- n! denotes the factorial of n, which is the product of all positive integers less than or equal to n.
Applying the formula, we have:
C(22, 9) = 22! / (9! * (22 - 9)!)
= 22! / (9! * 13!)
Calculating this expression, we find that there are 13,983,816 possible ways passengers can be chosen for the bus's first trip.