Computer keyboard failures can be attributed to electrical defects or mechanical defects. a repair facility currently has 25 failed keyboards 6 of which have electrical defects and 19 of which have mechanical defects. how many ways are there to randomly select 5 of these keyboards for a thorough inspection (without regard to order)?

You are going to select 5 keyboards, from a set of 25 defective keyboards. When you select the first keyboard it may be have either electrical deffects or mechanical deffect, this is two possibilities. The same happens with the second, third, fourth and fifth selection. Then  each selection has 2 different possibilities, and the number of possibilities are: 2*2*2*2*2 = 32.

But that is considering that the order matters. This is that it is different that the first has electrical deffects and the others have mechanical defects than the second has mechanical electrical deffects and the other has mechanical deffects.

If you the order is not relevant, then the only different outcomes are:

1) 5 with electrical deffects
2) 4 with electrical deffects and 1 with mechanical deffects
3) 3 with electrical deffects and 2 with mechanical deffects
4) 2 with electrical deffects and 3 with mechanical deffects
5) 1 with electrical deffects and 4 with mechanical deffects
5) 5 with mechanical deffects.

In this case the answer is 6 different ways.

6