Question

Please explain your answer as well. THX!!

Answer 1

Answer: Third option

`P = 0.354`

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:

`nCr = (n!)/(r!(n-r)!)`

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.

`12C4 = (12!)/(4!(12-4)!) = 495`

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.

`7C3 = (7!)/(3!(7-3)!) = 35`.

The possible combinations of selecting 1 a man from a group of 5 is

`5C1 = (5!)/(1!(5-1)!) = 5`

Then the number of ways in which 3 women and one man can be obtained is:

`7C3 * 5C1 = 35 * 5 = 175`

Finally the probability is:

P = Number of ways to obtain the desired result ÷ possible number of results

`P = (7C3 * 5C1)/(12C4)\\\\P = (175)/(495)`

`P = 0.354`