Question

You pick 5 cards out of a deck of 52. What is the probability that we get at least one card of each suit?

Answer 1

\[\frac{ \left(\begin{matrix}4 \\ 1\end{matrix}\right) \left(\begin{matrix}4 \\ 1\end{matrix}\right) \left(\begin{matrix}4 \\ 1\end{matrix}\right) \left(\begin{matrix}4 \\ 1\end{matrix}\right) \left(\begin{matrix}48 \\ 1\end{matrix}\right) }{ \left(\begin{matrix}52 \\ 5\end{matrix}\right) } \] is what i think it is, but i'm not sure

Answer 2

I was wrong last time. But i'm certain now the answer is
4 (13C2) (13C1) (13C1) (13C1) / (52C5) = 2197/8330

Answer 3

why is it 4 times all of all of that?

Answer 4

Actually, that makes sense! Thank you!

Answer 5

combination and permutation are really intimidating aren't they XD

Answer 6

Yeah it's the worst lol!