Probabilities of draws without replacement

Question

A history class is compromised of 4 female and 7 male students. If the instructor of the class randomly chooses 6 students from the class for an overall exam, what is the probability that 2 female students and 4 male students will be selected? Round your answer to 3 decimal places.

Answer 1

Hello Ashlee,

This problem involves combinations not permutations because the order in which the females (or the males) are selected makes no difference. For example, if I pick Mary and Juanita, it is the same as picking Juanita and Mary.

Since it is a probability question you will have a fraction. The denominator is all the possible ways you can pick 6 people from 11 (not considering if they are male or female). The numerator represents the way you want the 6 people to come out (2 females and 4 males). Where will the 2 females come from? Must pick 2 females from the 4 females. Where will the 4 males come from? Must pick 4 males from 7 males. Since the 2 females and 4 males you pick are parts or steps in the complete result, you multiply the number of ways to pick each of them.

All the choices will involve combinations. See if you can write the complete fraction with one combination in the denominator, and two combinations in the numerator. You can then use a calculator to find the decimal answer. If you write out the fraction and then get an answer, you can submit it for an expert to check your work.