Question 177065
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