# A bag contains contains 20 blue marbles, 20 green marbles, and 20 red marbles

A bag contains contains 20 blue marbles, 20 green marbles, and 20 red marbles.

Two marbles are drawn one after the other. no replacement

Using selection (combinations), find the probability of:

(a) drawing two marbles of the same colour

(b) drawing a blue and a green marble

(c) drawing a blue or a green marble

Would the sample space be P(60,2) or C(60,2)

• You can use either, but best is to choose $C(60,2)$... – Nicolas FRANCOIS Dec 14 '16 at 1:46

The question asks for combinations, but permutation seems more intuitive to me in this question, as the order of the marbles being drawn has to be taken into account.

I would use P(60,2) as the sample space. By doing so, I have to treat all 60 marbles as distinctive:
Blue: Marble 1, Marble 2, Marble 3..., Marble 20
Green: Marble 21, Marble 22, Marble 23..., Marble 40
Red: Marble 41 to Marble 60

(a) drawing two marbles of the same colour

$Probability = \frac{20P2+20P2+20P2}{60P2}$

(b) drawing a blue and a green marble

$Probability = \frac{(20P1*20P1)+(20P1*20P1)}{60P2}$

(c) drawing a blue or a green marble

$Probability = \frac{(20P1*40P1)+(20P1*40P1)}{60P2}$