how many different ways can 7 out of 18 people be picked to fit into a van
31824
To calculate the number of different ways to pick 7 out of 18 people to fit into a van, we can use the concept of combinations.
The formula for calculating combinations is:
C(n, k) = n! / (k! * (n-k)!),
where "n" represents the total number of people, and "k" represents the number of people to be picked.
Let's plug in the values:
n = 18 (total number of people)
k = 7 (number of people to be picked)
C(18, 7) = 18! / (7! * (18-7)!)
To simplify the calculation, let's first calculate the factorials:
18! = 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
(18-7)! = 11!
Now we can substitute the factorials into the formula:
C(18, 7) = 18! / (7! * 11!)
Calculating the factorials, we get:
C(18, 7) = 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (7 * 6 * 5 * 4 * 3 * 2 * 1 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Simplifying the expression, we see that many terms cancel out:
C(18, 7) = 18 * 17 * 16 * 15 * 14 * 13 * 12 / (7 * 6 * 5 * 4 * 3 * 2 * 1)
Evaluating the remaining terms:
C(18, 7) = 9,661,872
Therefore, there are a total of 9,661,872 different ways to pick 7 out of 18 people to fit into a van.