Assume that a committee consists of 12 people including the chairperson and that the chairperson must select a committee of 3 people from the other 11 members of the committee.
and the question is...?
In how many ways can this be done?
C(11,3) = 11*10*9/1*2*3 = 165
In this scenario, the chairperson needs to select a committee of 3 people from the remaining 11 members of the committee, excluding themselves. To find the total number of ways this can be done, we can use the concept of combinations.
The number of ways to select a committee of 3 people from a group of 11 can be calculated using the formula for combinations, which is given by:
C(n, r) = n! / (r!(n-r)!)
Here, n is the total number of objects to choose from (11 in this case), and r is the number of objects to be chosen (3 in this case).
Let's calculate this using the formula:
C(11, 3) = 11! / (3!(11-3)!)
= (11 * 10 * 9) / (3 * 2 * 1)
= 165
Therefore, there are 165 different ways for the chairperson to select a committee of 3 people from the remaining 11 members of the committee.