I've searched everywhere for a shortcut for this calculation on TI calculator, but can't find anything. X select Y, the formula is:
$$\frac{x!}{y!*(x-y)!}$$
Studying for test that has problems that require me to do this calculation a bunch of times, and it takes forever doing it manually.
The Best you can do:
(Example)
$$^{10}C_4=\frac{10!}{4!.6!}=\frac{10.9.8.7.6!}{4!.6!}=\frac{10*9*8*7}{4!}$$
Beyond this, only your speed can help you.