A bag contains 55 apples and 33 oranges. if you select 44 pieces of fruit without looking, how many ways can you get exactly 33 apples?

Given that the bag contains 5 apples and 3 oranges, if you select 4 pieces of fruit without looking, the number of ways you can get 3 apples is given by:

we can select 3 apples in 5C3 ways but we are selecting 4 pices, this means that one orange can be selected in 3c1 ways. Using product rule, the total ways to select four pices is

5C3*3C1

=5!/[3! * (5-1) !]*3!/[1! (3-1) !]

=120 / (6*2!) * 6 / (2!)

=12*3

=36