From a group of 5 men and 7 women, in how many different ways can a team of 2 men and 3 women be formed?
Correct Answer: C.350
2 men can be picked from a group of 5 in (5|2) = 10 different ways, and 3 women can be picked from a group of 7 in (7|3) = 35 different ways. Therefore, the total number of ways a team can be formed is 10 × 35 = 350.
Extended explanation: If you got D. 4200, you interpreted this problem as a permutation, not as a combination. We do not care what order the men are picked in or what order the women are picked in, all we care is that there is a team of 2 men and a team of 3 women.
Where n = total number of the group and r = the number of people we want. Hence,
n = 5 men
r = 2 men
We have 10 total possible combinations using the above formula.
The same goes for women.
n = 7 women
r = 3 women
We have 35 total possible combinations using the above formula.
Multiplied together, we have 350 possible combinations.
The Dental Admission Test (DAT) is a test administered by the American Dental Association (ADA). The test is four hours and 30 minutes long and contains four sections. The test is designed to assess your knowledge in: biology, chemistry, organic chemistry, perceptual ability, reading comprehension, and basic math.
How Should I Study?
The DAT is the final challenge before you apply to dental school and should not be taken lightly. Depending on the strength of your scientific knowledge, your study schedule should be between 4 to 10 weeks. Here's a link to my definitive DAT study guide and schedule which will help you prepare.
Register for the DAT.
You should plan on taking the DAT late spring or during the summer of your application year. For example, the class of 2020 should take the DAT in the spring or summer of 2015. You can begin the registration process for the DAT at the ADA's website. Be sure to apply for a test date early as the registration process may take some time.