A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from each class to be on a school board, how many different board can be selected?
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How would I go about this? Is this problem a combination?
since the three classes are separate, the combinations have to be calculated separately:
30C3 * 20C3 * 10C3 = 4060 * 1140 * 120 = _______
Ohh! Thank you so much!
Yes, this problem involves combinations. To find the number of different boards that can be selected, you can calculate the number of ways to choose 3 students from the senior class, 3 students from the junior class, and 3 students from the sophomore class. Then you can multiply these three numbers together to get the total number of different boards.
Yes, this problem involves combinations. To find the number of different boards that can be selected, we need to calculate the number of ways to choose 3 students from each class and then multiply those numbers together.
To find the number of ways to choose 3 seniors from a group of 30, we can use the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of students in the class and r is the number of students we want to choose.
So, for the seniors:
C(30, 3) = 30! / (3!(30-3)!) = 30! / (3! * 27!) = (30 * 29 * 28) / (3 * 2 * 1) = 4060
Similarly, we can calculate the number of ways to choose 3 juniors:
C(20, 3) = 20! / (3!(20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
And the number of ways to choose 3 sophomores:
C(10, 3) = 10! / (3!(10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Now, we can multiply these numbers together to find the total number of different boards that can be selected:
4060 * 1140 * 120 = 555,120,000
Therefore, there are 555,120,000 different boards that can be selected.