SOLUTION: In how many ways can a committee consisting of 2 faculty members and 5 students be formed if there are only 11 faculty members and 12 students eligible to serve on the committee?
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Question 1089768: In how many ways can a committee consisting of 2 faculty members and 5 students be formed if there are only 11 faculty members and 12 students eligible to serve on the committee? Answer by ikleyn(52832) (Show Source):
1. In how many ways can you select 2 members among 11 faculty members?
Since the order is not important, there are = = 55 ways.
2. In how many ways can you select 5 students among 12 students?
Since the order is not important, there are = = 792 ways.
3. Now, the selections among these two groups are independent.
Hence, in all , you have 55*792 ways in your global problem.
These magic numbers are called the numbers of combinations of n things taken k at a time.
