In how many ways can five balls be chosen so that.... In how many ways can five balls be chosen so that 
(a) two are red and three are black?
(b) three are red and two are black?
out of $7$ black and $8$ red
Should I use permutation?
or $8\times7\times7\times6\times5$?
And why?

You dont need to use permutation here because the ordering is not important .
You will have to choose combination here .
choosing $2$ red out of $8$ red = $_8C_2$ ways 
choosing $3$ black out of $7$ black = $_7C_3$ ways 
therefore total number of ways of doing (a)= $_8C_2 * _7C_3$ 
