A bag contains 2 red marbles 4 green ones 1 lavender one 3 y

A bag contains 2 red marbles, 4 green ones, 1 lavender one, 3 yellows, and 3 orange marbles.

How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?

Solution

Red    green   Lavender   Yellow   Orange   Total

2         4               1             3             3        13

Set of 5 marbles which contain either lavender one or exactly one yellow but not both

= 1C1(12C4)+3C1(10C4)-1C1(3C1)(10C3)

= 495+3*210-3(120)

= 1125-360

= 765