Una empresa desea contratar 3 nuevos

empleados, pero hay 8 candidatos, 6 de los

cuales son hombres y 2 son mujeres. Si la

seleccion es al azar:

a) 2De cuántas maneras diferentes se pueden

elegir los nuevos empleados?

b) De cuántas maneras distintas se puede

elegir a un solo candidato hombre?

c) De cuántas maneras distintas se puede

elegir por lo menos a un candidato horribre?

Rptas a) 56 b) 6 c) 56

A company wants to select 3 new employees.

We have 8 candidates, 6 males, and 2 females.

1) What is the number of combinations in which the new employees can be selected?

We have 3 positions.

For the first position, we have 8 options.

For the second position, we have 7 options, because we already selected one.

For the third position, we have 6 options, because we already selected two.

The number of different combinations is (8*7*6) / (3*2*1) = 56

The division by 3*2*1 is because if we no divide by this, we are counting multiple times the same combination of employees, but they are contracted in different orders.

2) How many ways you can select only one male?

In this case, we have 3 positions, two of those positions must be for the 2 women, so in the other position, we can select only one male.

We have 6 different males for that position, so we have only 6 combinations in this case.

3) In how many ways we can select at least one male?

Previously found that we have 56 combinations in total.

We only have 2 women and 3 positions, so in all of these combinations, we have at least one male. So there are 56 combinations with at least one male.