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need help with b

I need help with B, I have A (15 P 5)

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    $~_{15}P_5$ (*also written as $15\frac{5}{~}, \frac{15!}{10!}, 15\cdot 14\cdots 11, P(15,5)$*) is indeed the correct answer for (A) (*assuming that every position is considered distinct... I don't know basketball as well as I know mathematics, but that seems like a safe assumption*). – 2017-01-27

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Approach via multiplication principle.

  • Pick who the center is: You have two options

  • Pick who the power forward is: You have $14$ remaining options since it can't be who you picked for the center

  • Pick who the small forward is: You have $13$ remaining options since it can't be either of the two previously selected people

  • Pick who the point guard is: $12$ remaining options

  • Pick who the shooting guard is: $11$ remaining options

The answer then is $2\cdot 14\cdot 13\cdot 12\cdot 11$

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    what if I didnt know what a point guard, shooting guard, etc was in basketball? Why did you stop at 11? – 2017-01-27
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    Multiplication principle, a.k.a. [Rule of Product](https://en.wikipedia.org/wiki/Rule_of_product) states that if you can describe **every** outcome with via a sequence of questions/choices such that **every** outcome is achieved by **exactly one** sequence of choices and each sequence of choices yields **exactly one** outcome and the number of choices for each step doesn't change based on the previously made choices, then the total number of outcomes is the product of the number of choices at each step. – 2017-01-27
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    @keving if you don't know anything about basketball, then state what assumptions you are making when writing your answer. In this case, I **assume** that each position in basketball is unique and it matters who is in what position as well as who is playing. You would be equally correct if you said the answer to (A) was $~_{15}C_5$ instead if you stated that you assumed that positions didn't matter., but that wouldn't make sense considering the wording of the second part and them specifying that there is a unique position called "center" – 2017-01-27