SOLUTION: A class contains 7 women and 7 men. Suppose we choose three random students. How many ways can we choose exactly 1 woman?
I am very confused with this. I have gotten differen
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Question 529143: A class contains 7 women and 7 men. Suppose we choose three random students. How many ways can we choose exactly 1 woman?
I am very confused with this. I have gotten different ways to solve and different answers for this.
Please help. I have to turn this homework in tomorrow.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
It depends. Does the order in which the selection is made make a difference? That is to say is a three student group that is chosen in the order Bill, Tom, and Alice the same or different from one was chosen in the order Tom, Alice, and Bill?
Order matters: Number of permutations of 7 things taken 1 at a time TIMES permutations of 7 things taken 2 at a time:
!}\right)\left(\frac{7!}{(7-2)!}\right)\ =\ \left(\frac{7!}{6!}\right)\left(\frac{7!}{5!}\right)\ =\ 7\ \times\ 7\ \times\ 6)
Order does not matter: Number of combinations of 7 things taken 1 at a time TIMES the number of combinations of 7 things taken 2 at a time:
!}\right)\left(\frac{7!}{2!(7-2)!}\right)\ =\ \left(\frac{7!}{6!}\right)\left(\frac{7!}{2!5!}\right)\ =\ 7\ \times\ 7\ \times\ 3)
John
My calculator said it, I believe it, that settles it
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