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.
In how many ways can this be done?
There are 12 ways to pick a chairman, and then we have to choose 3 of the remaining 11
number of ways = 12*C(11,3)
= 12(165) = 1980
i tried that already and its not the right answer :(..
To find the number of ways the chairperson can select a committee of 3 people from the other 11 members, we can use the concept of 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 you want to select.
In this case, there are 11 members that the chairperson can choose from and the chairperson needs to select a committee of 3 people.
Using the formula, we can calculate the number of ways:
C(11, 3) = 11! / (3!(11-3)!)
Simplifying further:
C(11, 3) = 11! / (3! * 8!)
Now, let's calculate the factorials:
11! = 11 * 10 * 9 * 8! = 11 * 10 * 9 * (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
3! = 3 * 2 * 1
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
Substituting the factorials back into the formula:
C(11, 3) = (11 * 10 * 9 * (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)) / ((3 * 2 * 1) * (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1))
Simplifying further:
C(11, 3) = (11 * 10 * 9) / (3 * 2 * 1)
Cancelling out some terms:
C(11, 3) = (11 * 10 * 9) / 6
Doing the multiplication:
C(11, 3) = 990 / 6 = 165
Therefore, there are 165 ways the chairperson can select a committee of 3 people from the other 11 members of the committee.