Question

Determine whether the statement takes sense or does not make sense, and explain your reasoning.

When finding the probability of randomly selecting 2 men and 1 woman from a group of 10 men and 10 women, I used the formula for 6, 3 times,
Choose the correct answer below.
A. This statement does not make sense. The formula for C, is used once, to find the number of combinations of 3 people out of the whole group
B. This statement makes sonso. The formula for C, is used to find the number of combinations of 2 man out of the 10 men, the number of combinations of a woman out of the 10 women, and the number of combinations of 3 people out of
the whole group
C. This statement makes sense. The formula for C, is used to find the number of combinations of 2 men out of the whole group, the number of combinations of 1 woman out of the whole group, and the number of combinations of 3 people
out of the whole group
D. This statement does not make sense. The formula for Gr is used twice, to find the number of combinations of 2 men and 1 woman out of the whole group, and to find the number of combinations of 3 people out of the whole group.

Answer 1

The statement about using the formula for 6 choose 3 times is incorrect. The correct approach uses the combination formula separately for the two groups, 10 choose 2 for men and 10 choose 1 for women, then multiplying the results.

Step-by-step explanation:

The statement that uses the formula for 6 choose 3 times does not make sense for calculating the probability of randomly selecting 2 men and 1 woman from a group of 10 men and 10 women. The correct approach would be to use the combination formula separately for men and women.

To find the number of combinations of 2 men out of 10, we use 10 choose 2. For 1 woman out of 10, it's 10 choose 1. Then, these two results are multiplied together to find the total number of combinations for selecting 2 men and 1 woman. The probability is then calculated by dividing this product by the total number of ways to choose any 3 people from the group of 20. Thus, the correct answer is:

A. This statement does not make sense. The formula for C, is used once, to find the number of combinations of 3 people out of the whole group