8 people in the playground. How many ways can 6 people be selected to play?
Find the rule.
To find the number of ways that 6 people can be selected from a group of 8, we need to use the concept of combinations. The formula for combinations, also known as "n choose k," is given by:
C(n, k) = n! / (k!(n-k)!)
Where "n" represents the total number of people in the group, and "k" represents the number of people to be selected.
In this case, we have 8 people in the playground and we want to select 6 of them. Applying the formula:
C(8, 6) = 8! / (6!(8-6)!)
Calculating the factorial values:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1
2! = 2 * 1
Substituting the values into the formula:
C(8, 6) = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(6 * 5 * 4 * 3 * 2 * 1) * (2 * 1)]
Simplifying:
C(8, 6) = (8 * 7) / (2 * 1) = 28
Therefore, there are 28 ways to select 6 people to play from a group of 8.