For a mock United Nations, 6 students from class A and 7 students from class B are to be chosen. If there are 12 students from class A and 9 students from class B to choose from, how many groups are possible?
Question
For a mock United Nations, 6 students from class A and 7 students from class B are to be chosen. If there are 12 students from class A and 9 students from class B to choose from, how many groups are possible?
Solution
To solve this problem, we need to use the combination formula which is C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
Step 1: Calculate the number of ways to choose 6 students from class A. Here, n = 12 (total students in class A) and r = 6 (students to be chosen from class A). So, C(12, 6) = 12! / [(12-6)! * 6!] = 924 ways.
Step 2: Calculate the number of ways to choose 7 students from class B. Here, n = 9 (total students in class B) and r = 7 (students to be chosen from class B). So, C(9, 7) = 9! / [(9-7)! * 7!] = 36 ways.
Step 3: Since the students can be chosen from class A and class B independently, we multiply the number of ways to get the total number of groups possible. So, the total number of groups = 924 * 36 = 33,264 groups.
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