You are picking a team of 5 people from a group of 7. How many ways can you do it?
There are 21 ways you can pick a team of 5 people from a group of 7.
This can be calculated using the combination formula:
nCr = n! / r!(n-r)!
In this case, n is 7 (the total number of people) and r is 5 (the number of people being picked for the team).
7C5 = 7! / 5!(7-5)!
= 7! / 5!2!
= (7 x 6 x 5 x 4 x 3) / (2 x 1)
= 21
Therefore, there are 21 ways you can pick a team of 5 people from a group of 7.
To calculate the number of ways you can pick a team of 5 people from a group of 7, you can use combinations. The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items and r is the number of items to be chosen.
In this case, you need to find C(7, 5). Substituting the values into the formula, we get:
C(7, 5) = 7! / (5! * (7 - 5)!)
Calculating further:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
5! = 5 * 4 * 3 * 2 * 1 = 120
Substituting these values:
C(7, 5) = 5040 / (120 * 2)
C(7, 5) = 5040 / 240
Simplifying the expression:
C(7, 5) = 21
Therefore, there are 21 ways to pick a team of 5 people from a group of 7.