In general the answer to "I pull n balls from a bag with B black balls and R red balls; how many are black?" is a Hypergeometric distribution.
. In Wikipedia's notation, N=total number of balls, K=number of red balls, n=number of balls you draw, k=number of red balls you get.
For your specific problem, as heehaww said,
4 black: 10 ways out of 56
3 black 1 red: 30 ways out of 56
2 black 2 red: 15 ways out of 56
1 black 3 red: 1 way out of 56
all 4 red obvious impossible.