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:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
3 cinnamon, from a set of 6.
2 peppermint, from a set of 5. So
[tex]D = C_{6,3}*C_{5,2} = \frac{6!}{3!(6-3)!}*\frac{5!}{2!(5-2)!} = 200[/tex]
Total outcomes:
5 candies, from a set of 6+5+7 = 18. So
[tex]T = C_{18,5} = \frac{18!}{5!(18-5)!} = 8568[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{200}{8568} = 0.0233[/tex]
2.33% probability that three are cinnamon and two are peppermint
