SOLUTION: A bag contains a red, a blue, a yellow, a white, and a green ball. Three balls are drawn out without replacement. a.) What is the probability that the red and yellow ball are

Question 177065: A bag contains a red, a blue, a yellow, a white, and a green ball. Three balls are drawn out without replacement.
a.) What is the probability that the red and yellow ball are selected?
B.) What is the probability that the two balls are selected in the order listed (red, yellow)?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a) the number of possible triplets (3) from a group of five is 5C3 (order is NOT important)

5C3 = 5! / (3! * 2!) = 120 / (6 * 2) = 10

the red and yellow can be combined with any of the 3 other colors, so there are 3 triplets containing red & yellow

the probability of red & yellow is 3 in 10 or .3

b) the number of triplets from a group of 5 if order IS important is 5P3

5P3 = 5! / 2! = 120 / 2 = 60

again, the red & yellow can be combined with each of the other 3 colors
__ but each of the resulting 3 triplets can be arranged in 6 ways (3 * 2 * 1)

of the 6 ways, only 2 have the red & yellow in the proper order; either preceded by or followed by the 3rd color

this means that 6 out of the 60 possible triplets have red & yellow in the proper order

6 in 60 is a probability of .1
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