Question

How many 6 card hands containing no queens and no spades can be chosen from a bridge deck of 52 card?

Answer 1

So if there are no queens (4 queens) and no spades (12 spades not including the spade queen) , there are
52-12-4=36 total cards.

Then it's 36 choose 6
\[ \text{possible combos}=\left( \begin{array}{c} 36 \\ 6\end{array}\right) = \frac{36!}{6!(36-6)!}=\frac{36\times35 \times 34\times33 \times 32\times 31}{6\times 5 \times 4 \times 3 \times 2 \times 1}\]

Answer 2

Seems right to me. Nice.