A committee must be formed with 4 teachers and 4 students. If there are 6 teachers to choose from, and 12 students, how many different ways could the committee be made?
so if the answer is (6,4) *(12,4)
do i multiply these?
yes, if you mean C(6,4)*C(12,4)
To find the total number of ways to form the committee, you need to multiply the number of ways to choose the teachers and the number of ways to choose the students.
In this case, you want to choose 4 teachers from a pool of 6, which can be represented as "6 choose 4." Similarly, you want to choose 4 students from a pool of 12, which can be represented as "12 choose 4."
So to calculate the total number of ways, you multiply the two values together:
(6 choose 4) * (12 choose 4)
The expression "(n choose k)" represents the number of ways to choose k items from a pool of n items, and it can be calculated using the binomial coefficient formula:
n! / (k! * (n - k)!)
where "!" denotes the factorial operation.
To find the total number of ways to form the committee with 4 teachers and 4 students, you need to calculate the product of the number of ways to choose the teachers and the number of ways to choose the students separately.
So the number of ways to choose 4 teachers from 6 would be denoted as "6 choose 4", which is calculated as:
(6 choose 4) = 6! / (4! * (6-4)!) = 6! / (4! * 2!) = (6 * 5) / (2 * 1) = 15
Similarly, the number of ways to choose 4 students from 12 would be denoted as "12 choose 4", which is calculated as:
(12 choose 4) = 12! / (4! * (12-4)!) = 12! / (4! * 8!) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1) = 495
Now to find the total number of ways to form the committee, you multiply these two values together:
Total number of ways = (6 choose 4) * (12 choose 4) = 15 * 495 = 7425
So there are 7425 different ways the committee can be formed.