Question

A deck of cards contains 6 black cards numbered 5 to 10 and 6 red cards numbered 1 to 6. How many 5-card hands having 3 black cards and 2 red cards can be dealt?

Answer 1

What do you think?

Answer 2

I think it is 65 but not positive

Answer 3

The number of combinations of the 6 black cards, taken 3 at a time, is given by
\[\large 6C3=\frac{6!}{3!3!}\]
The number of combinations of the 6 red cards, taken 2 at a time, is given by
\[\large 6C2=\frac{6!}{2!4!}\]
Each combination of black cards can be taken with each combination of red cards.
Therefore the total number of combinations is given by
\[\large 6C3 \times 6C2=you\ can\ calculate\]

Answer 4

I got 300, thanks!

Answer 5

You're welcome :)