Question

Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 12 of which have electrical defects and 13 of which have mechanical defects. (a) How many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to order)

Answer 1

There are 177,100 ways.

Explanation:

Since there is no regard to order, we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In this question:

6 keyboards from a set of 25. So

`C_(25,6) = (25!)/(6!(25-6)!) = 177100`

There are 177,100 ways.