Question

There are 12 seniors, 10 juniors, 5 sophomores, and 3 freshmen on the student council. A committee of 7 members is formed. Determine the number of ways to form this committee given the following conditions: the committee must have 3 seniors, 2 juniors, 1 sophomore, and 1 freshman.

a) 7,291,200 ways
b) 12 ways
c) 1,021,200 ways
d) 72,912 ways

Answer 1

To form the committee, we calculate the number of ways to select the required number of students from each grade level and multiply them together. The correct answer is 1,021,200 ways.

Step-by-step explanation:

To determine the number of ways to form the committee, we need to consider the number of ways to select the required number of students from each grade level.

For the seniors, there are 12 students and we need to select 3 of them. This can be done in C(12, 3) ways.

Similarly, for juniors, there are 10 students and we need to select 2 of them, which can be done in C(10, 2) ways. For sophomores, there are 5 students and we need to select 1 of them, which can be done in C(5, 1) ways. And finally, for freshmen, there are 3 students and we need to select 1 of them, which can be done in C(3, 1) ways.

To find the total number of ways to form the committee, we need to multiply the number of ways for each grade level: C(12, 3) * C(10, 2) * C(5, 1) * C(3, 1).

Simplifying the expression, we get 220 * 45 * 5 * 3 = 1,021,200 ways.

Therefore, the correct answer is c) 1,021,200 ways.