Three students from a 21 student class will be selected to attend a meeting. 8 of the students are female.
What is the probability that all three of the students chosen to attend the meeting are female? =
To find the probability that all three students chosen to attend the meeting are female, we need to determine the ratio of the number of favorable outcomes to the number of possible outcomes.
In this scenario, the number of favorable outcomes is the number of ways to choose 3 students from the 8 female students in the class, which is given by the combination formula:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of objects to choose from, and r is the number of objects to be chosen.
So, the number of ways to choose 3 students from 8 female students is:
C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
The number of possible outcomes is the total number of ways to choose 3 students from the 21 students in the class. This can also be calculated using the combination formula:
C(21, 3) = 21! / (3!(21-3)!) = 21! / (3!18!) = (21 * 20 * 19) / (3 * 2 * 1) = 1330
Finally, the probability that all three of the students chosen to attend the meeting are female is:
Probability = favorable outcomes / possible outcomes = 56 / 1330 ≈ 0.0421
So, the probability is approximately 0.0421 or 4.21%.