How many different basketball teams can be formed from a squad of 12 men if only 2 of the men can play center and these two can play in no other position?
My answer is
$N$= $10C4$ $\cdot$ $2C1$ = $420$ teams
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1How many ways can you choose a center? How many ways can you choose the other four players? Multiply these two numbers. – angryavian Jan 01 '18 at 04:11
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10C4 x 2C1 is this correct? – Madisson Jan 01 '18 at 04:19
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@Madisson It's not about whether you got to the answer - it's about how you got to the answer. Please show your work and put it in your question. – Toby Mak Jan 01 '18 at 06:21
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We have $12$ player, in particular $10$ of them can play everywhere while $2$ have a fixed position. First we do all the calculation considering only $1$ center and finally we are going to multiply by $2$ our partial results.
We know that each team is made of $5$ people. We fix the one who must play as a center and we have $\binom{10}{4}$ possibility to choose the other four player. This means that, at the end, we have: $$\binom{10}{4}\cdot 2=210\cdot 2=420$$ possible teams.