Question

Find probabilities using combinations and permutations. Tyler was feeling particularly adventurous at the hair salon one day, and decided to dye his hair. The stylist informed him that he had 10 colors to choose from, 6 of which were shades of purple . If Tyler randomly selects 5 colors and tells the stylist to choose from those, what is the probability that exactly 2 of the chosen hair dyes are shades of purple? Write your answer as a decimal rounded to four decimal places.

Answer 1

There are total of 10 colors to choose.

6 are shades of purple and

4 are not shades of purple.

Tyler selects 5 colors, and exactly 2 are shades of purple. Therefore, the 3 other colors are not shades of purple.