MATH SOLVE

2 months ago

Q:
# A pack of confectioneries contains candies in four (4) flavors (berry, lemon, orange and cacao), 3 pieces each. Candies are distributed randomly in the pack. You draw the first three (3) pieces from the pack. What is the probability that they are all different flavors?

Accepted Solution

A:

Answer:The probability is 0.4909Step-by-step explanation:The following equation for nCk give as the number of ways in which we can select k elements from a group of n elements:[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]Then, there are 220 ways in which we can select 3 candies from the 12 that are in the pack. It is calculated as:[tex]12C3=\frac{12!}{3!(12-3)!}=220[/tex]On the other hand, there are 108 different ways to select the 3 candies in which they are all different flavors. It is calculated as:4C3 * 3C1 * 3C1 * 3C1 = 108Because, 4C3 give us the number of ways to select 3 flavors from the 4 flavors. From this 3 flavors selected, we are going to select one candie from each one, so we multiply 3 times by 3C1, one for each flavor.Finally, the probability is the division between the number of ways in which we can select 3 candies with different flavors and the total number of ways in which we can select 3 candies from the 12 in the pack. This is:[tex]P=\frac{108}{220}=0.4909[/tex]