7 freshmen, 10 sophomores, 7 juniors, and 8 seniors are eligible to be on a committee.
In how many ways can a dance committee of 18 students be chosen?
In how many ways can a dance committee be chosen if it is to consist of 5 freshmen, 6 sophomores, 4 juniors, and 3 seniors.
32 students in all, so 32C18 ways to make a committee
Using the criteria given, there would be 7C5 * 10C6 * 7C4 * 8C3 ways
similarly for the board, 30C20 or 10C3 * 20C17
There are 10 female board members and 20 male board members.
How many ways are there to make a committee of 20 board members?
How many ways are there to make a committee of 20 board members if exactly 3 must be female?
There are 13 female board members and 17 male board members.
How many ways are there to make a committee of 18 board members?
How many ways are there to make a committee of 18 board members if exactly 6 must be female?
7 freshmen, 7 sophomores, 8 juniors, and 9 seniors are eligible to be on a committee.
In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 4 sophomores, 5 juniors, and 3 seniors.
To find the number of ways to choose a dance committee, we need to apply the concept of combinations. In this scenario, we have a total of 32 students: 7 freshmen, 10 sophomores, 7 juniors, and 8 seniors.
1. In how many ways can a dance committee of 18 students be chosen?
To find the number of ways to choose 18 students from the total 32, we can use the concept of combinations. 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 chosen.
In this case, n = 32 (total number of students) and r = 18 (number of students to be chosen for the dance committee).
Using the formula, the calculation would be:
C(32, 18) = 32! / (18!(32-18)!)
2. In how many ways can a dance committee be chosen if it consists of 5 freshmen, 6 sophomores, 4 juniors, and 3 seniors?
In this case, we need to choose a specific number of students from each grade level. This is known as a multi-combination.
To find the number of ways, we can calculate the combinations for each grade level and then multiply them together. The formula for the multi-combination is:
C(n1, r1) * C(n2, r2) * C(n3, r3) * C(n4, r4)
Where n1, n2, n3, n4 are the total number of students in each grade level, and r1, r2, r3, r4 are the number of students to be chosen from each grade level.
In this case, n1 = 7 (freshmen), n2 = 10 (sophomores), n3 = 7 (juniors), n4 = 8 (seniors). And r1 = 5 (freshmen to be chosen), r2 = 6 (sophomores to be chosen), r3 = 4 (juniors to be chosen), r4 = 3 (seniors to be chosen).
The calculation would be:
C(7, 5) * C(10, 6) * C(7, 4) * C(8, 3)