A class consists of 16 boys,12girls, and 2 teachers. How many different committees of size eight can be formed if the committee must consist of 4 boys 3 girls and one teacher?
Choose 4 boys from 16 = C(16,4) = 1820
choose 3 girls from 12 = C(12,3) = 220
choose 1 teacher from 2 = C(2,1) = 2
no. of committees = 1820x220x2 = 800800
To find how many different committees of size eight can be formed with specific criteria, we can use the concept of combinations.
We need to select 4 boys from the group of 16, 3 girls from the group of 12, and 1 teacher from the group of 2.
The number of ways to select 4 boys from 16 can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items to choose from, and r is the number of items to choose.
For selecting 4 boys from 16, we can calculate it as:
C(16, 4) = 16! / (4! * (16 - 4)!)
Similarly, the number of ways to select 3 girls from 12 and 1 teacher from 2 can be calculated as:
C(12, 3) = 12! / (3! * (12 - 3)!)
C(2, 1) = 2! / (1! * (2 - 1)!)
To find the total number of committees that satisfy the criteria, we need to multiply these combinations together:
Total number of committees = C(16, 4) * C(12, 3) * C(2, 1)
By calculating this expression, we can obtain the final answer.