Question

A refrigerator contains 6 cans of diet soda and 7 cans of regular soda. if three cans of soda are randomly selected without​ replacement, determine the probability that all cans selected are diet soda. use combinations to determine the probability. question content area bottom part 1 the probability that all cans selected are diet soda is enter your response here. ​(type an integer or a simplified​ fraction.)

Answer 1

To determine the probability of selecting all diet soda cans, we need to calculate the number of possible combinations of selecting 3 cans from the total number of cans and divide it by the total number of possible combinations of selecting 3 cans from all the cans. The probability is 10/143.

Step-by-step explanation:

To determine the probability of selecting all diet soda cans, we need to calculate the number of possible combinations of selecting 3 cans from the total 13 cans in the refrigerator, and then divide it by the total number of possible combinations of selecting 3 cans from all the cans in the refrigerator.

The total number of possible combinations of selecting 3 cans from 13 cans is given by the formula C(13, 3) = 13! / (3! * (13 - 3)!), which simplifies to 286.

The total number of possible combinations of selecting 3 cans from 13 cans of diet soda is given by the formula C(6, 3) = 6! / (3! * (6 - 3)!), which simplifies to 20.

Therefore, the probability that all cans selected are diet soda is 20/286, which can be simplified to 10/143.