6 teachers and 12 students volunteer for a committee to discuss extra curricular activities. How many committees of 5 people can be made if there are no restrictions
Since there are no restrictions, we can select any 5 people out of the total 18 people (6 teachers + 12 students). This can be calculated using the combination formula:
C(18, 5) = 18! / (5!(18-5)!) = 8568
Therefore, there can be 8,568 different committees of 5 people.
To find the number of committees that can be made without any restrictions, we will use the concept of combinations.
In this case, we need to choose 5 people out of a total of 6 teachers and 12 students. The order in which they are chosen does not matter.
The formula for combinations is:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items and r is the number of items to be selected.
Using this formula, we can calculate the number of committees:
C(18, 5) = 18! / (5! * (18 - 5)!)
= (18 * 17 * 16 * 15 * 14) / (5 * 4 * 3 * 2 * 1)
= 18 * 17 * 16 * 15 * 14 / 5 * 4 * 3 * 2 * 1
= 102,816
Therefore, there are 102,816 committees of 5 people that can be made without any restrictions.