1) A bag contains three red marbles, six green ones, one lavender one, four yell

Question

1) A bag contains three red marbles, six green ones, one lavender one, four yellows, and two orange marbles.
How many sets of four marbles include all the red ones?

2) A bag contains two red marbles, three green ones, one lavender one, six yellows, and four orange marbles.
How many sets of five marbles include one of each color?

3) A bag contains four red marbles, two green ones, one lavender one, three yellows, and two orange marbles.
How many sets of five marbles include at most one of the yellow ones?

Explanation / Answer

3 Red, 6 Green, 1 Lavender, 4 yellow, 2 Orange

1)
If 4 marbles are selected, combinations where all 3 red ones are selected are 13C1 i.e. 13 combinations

2)
2 Red, 3 Green, 1 Lavender, 6 yellow, 4 Orange
Possible combinations are 2*3*1*6*4 = 144

3)
4 Red, 2 Green, 1 Lavender, 3 yellow, 2 Orange
Combinations that has no yellow marble, 9C5
Combinations that has 1 yellow marble, 8C4*3C1

Required combinations are 9C5*8C4*3C1 = 26460

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