# Coach Ringdahl has 10 players on his varsity basketball team.

Coach Ringdahl has 10 players on his varsity basketball team. How many different starting line-ups (5 players) can he choose?
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Step 1
This is a combinations question - we don't care about the order in which we select the 5 players in the starting line-up, only that they are chosen.
So we have: ${C}_{10,5}=\frac{10!}{\left(5!\right)\left(10-5\right)!}=\frac{10!}{\left(5!\right)\left(5!\right)}$
Step 2
And now let's evaluate this: $\frac{10!}{\left(5!\right)\left(5!\right)}=\frac{\overline{)10}×{\overline{)9}}^{3}×{\overline{)8}}^{2}×7×6×\overline{)5}!}{\left(\overline{)5}!\right)\left(\overline{)5}×\overline{)4}×\overline{)3}×\overline{)2}×1\right)}=3×2×7×6=252$
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