Question

In a group of 16 people, 7 are left handed and the rest are right handed. If 6 people are selected at random, in how many ways may all right handed people be selected?

Answer 1

There are 84 different ways to select 6 people, all right-handed, from a group of 16 people with 9 right-handed individuals, calculated using the combination formula C(n, k).

Step-by-step explanation:

The question relates to the field of combinatorics in mathematics, specifically the calculation of combinations when selecting items from different groups without replacement. In this case, we have a total of 16 people with 7 left-handed and 9 right-handed individuals. We want to find out how many different ways we can choose 6 people, all of whom are right-handed.

To solve this, we use the combination formula C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, k is the number of items to choose, ! is the factorial operator, and C(n, k) represents the number of combinations of n items taken k at a time. Since all selected individuals are to be right-handed, we only consider the group of 9 right-handed people:

1. Calculate the number of combinations of selecting 6 people from 9, which is C(9, 6).
2. Apply the formula: C(9, 6) = 9! / (6! * (9 - 6)!) = 9! / (6! * 3!)
3. Calculate the factorials: 9! = 9 * 8 * 7 * 6! and 3! = 3 * 2 * 1.
4. Simplify and get the result: (9 * 8 * 7) / (3 * 2 * 1) = 84 ways.

Therefore, there are 84 ways to select 6 people, all right-handed, from a group of 16 people with 9 right-handed individuals.