Question

Two companies have sent representatives to an industry conference. The first company sent 12 representatives and the

second company sent 20 representatives. Only 22 will be given the chance to make presentations. What is the probability
that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen?
Select the correct answer below:

Answer 1

The probability of exactly 10 representatives from the first company and 12 representatives from the second company being chosen out of the total of 22 representatives can be calculated using combinations.

Step-by-step explanation:

The probability of exactly 10 representatives from the first company and 12 representatives from the second company being chosen out of the total of 22 representatives is calculated using the concept of combinations.

First, let's determine the total number of ways to choose 22 representatives from the combined total of 12 representatives from the first company and 20 representatives from the second company:

C(12+20, 22) = C(32, 22) = 32! / (22! * (32-22)!) = 32! / (22! * 10!)

Next, let's determine the number of ways to choose 10 representatives from the first company and 12 representatives from the second company:

C(12, 10) * C(20, 12) = (12! / (10! * (12-10)!) * (20! / (12! * (20-12)!)

Finally, let's calculate the probability by dividing the number of favorable outcomes (number of ways to choose 10 representatives from the first company and 12 representatives from the second company) by the total number of possible outcomes:

Probability = (C(12, 10) * C(20, 12)) / (C(32, 22))

Let's substitute the values and calculate:

Probability = (12! / (10! * (12-10)!) * (20! / (12! * (20-12)!)) / (32! / (22! * (32-22)!))

This gives us the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen out of the total of 22 representatives.