Question

A jar of candy has 6 cinnamon, 5 peppermint and 7 spearmint candies in it. Your pick five pieces of candy out of the jar at the same time. What is the probability that three are cinnamon and two are peppermint?

Answer 1

Answer:

2.33% probability that three are cinnamon and two are peppermint

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the candies are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

3 cinnamon, from a set of 6.

2 peppermint, from a set of 5. So

$D = C_{6,3}*C_{5,2} = \frac{6!}{3!(6-3)!}*\frac{5!}{2!(5-2)!} = 200$

Total outcomes:

5 candies, from a set of 6+5+7 = 18. So

$T = C_{18,5} = \frac{18!}{5!(18-5)!} = 8568$

Probability:

$p = \frac{D}{T} = \frac{200}{8568} = 0.0233$

2.33% probability that three are cinnamon and two are peppermint