A sales force has 10 men and 10 women. A production unit of 7 people is set up at random. What is the probality that it will consist of 3 men and 4 women
To find the probability of forming a production unit consisting of 3 men and 4 women out of a sales force of 10 men and 10 women, we need to first find the total number of ways to form a production unit and then determine the number of favorable outcomes.
The total number of ways to form a production unit of 7 people can be calculated using combinations. We can choose 7 people out of the total sales force of 20 people. This can be represented as:
C(20, 7) = (20!)/(7!(20-7)!) = 77520
Now, let's determine the number of favorable outcomes, i.e., the number of ways to select 3 men and 4 women from their respective groups.
The number of ways to select 3 men from a group of 10 is:
C(10, 3) = (10!)/(3!(10-3)!) = 120
Similarly, the number of ways to select 4 women from a group of 10 is:
C(10, 4) = (10!)/(4!(10-4)!) = 210
To get the number of favorable outcomes, we multiply the number of ways to select 3 men by the number of ways to select 4 women:
Favorable outcomes = C(10, 3) * C(10, 4) = 120 * 210 = 25200
Therefore, the probability of forming a production unit consisting of 3 men and 4 women is given by:
Probability = Favorable outcomes / Total outcomes
Probability = 25200 / 77520
Probability ≈ 0.325