Combinations Help Urgent (1 Viewer)

[csi]

Hi,

Can someone please help with this question:
A small company has 55 employees: 4 senior executives, 15 managers and 36 non-executives. A group of 5 employees are chosen at random, what is the probability that there are exactly 2 senior executives in the group?

Answer: 0.036

Thanks!

 

[ExtremelyBoredUser]

Hi,

Can someone please help with this question:
A small company has 55 employees: 4 senior executives, 15 managers and 36 non-executives. A group of 5 employees are chosen at random, what is the probability that there are exactly 2 senior executives in the group?

Answer: 0.036

Thanks!

The total ways you can choose any employee out of the business is 55C5. This will be the denom.

There are 4 senior executives, we only want 2 in the group. 4C2
Now to ensure we don't get any more senior executives, we only consider the remaining batch (55-4 =51). Choose any 3 from there. 51C3


4C2 * 51C3/55C5 = 0.036 to 2dp

 

[csi]

The total ways you can choose any employee out of the business is 55C5. This will be the denom.

There are 4 senior executives, we only want 2 in the group. 4C2
Now to ensure we don't get any more senior executives, we only consider the remaining batch (55-4 =51). Choose any 3 from there. 51C3


4C2 * 51C3/55C5 = 0.036 to 2dp

thanks