Question

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?

Answer 1

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