the problem asks:

a bag contains 5 aplles and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get exactly 3 apples?

so i did:

"c"=stands for combination

(5C3) =10
(3C1) = 6

so i multiplied 10*6 = 60 ways possible

It seems to me it is not that...
Ways to get apples
AAAO
AAOA
AoAA
OAAA

so what do you refer too

60 ways sounds right to me.
You could have
A1,A2,A3,O1
A1,A2,A3,O2
A1,A2,A3,O3
A1,A2,A4,O1
......
......
......
A6,A7,A8,O3

Of course, I presume order doesnt matter.