Answer: Third option
[tex]P = 0.354[/tex]
Step-by-step explanation:
We have an elevator with 5 men and 7 women. We want to find the probability that 3 women and one man will come down from the elevator.
To calculate this probability we can use combinations.
The formula of combinations is:
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
Where you can choose between n people and choose r from them.
First we calculate all the possible results of the experiment.
That is, the amount of ways to select 4 people from a group of 12 people.
[tex]12C4 = \frac{12!}{4!(12-4)!} = 495[/tex]
There are 495 results.
Now we calculate the possible number of ways to obtain the desired result, that is 3 women and one man.
The possible combinations of selecting 3 women from a group of 7 is.
[tex]7C3 = \frac{7!}{3!(7-3)!} = 35[/tex].
The possible combinations of selecting 1 a man from a group of 5 is
[tex]5C1 = \frac{5!}{1!(5-1)!} = 5[/tex]
Then the number of ways in which 3 women and one man can be obtained is:
[tex]7C3 * 5C1 = 35 * 5 = 175[/tex]
Finally the probability is:
P = Number of ways to obtain the desired result ÷ possible number of results
[tex]P = \frac{7C3 * 5C1}{12C4}\\\\P = \frac{175}{495}[/tex]
[tex]P = 0.354[/tex]
