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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)

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Answer:

There are 177,100 ways.

Step-by-step explanation:

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

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

6 keyboards from a set of 25. So

[tex]C_{25,6} = \frac{25!}{6!(25-6)!} = 177100[/tex]

There are 177,100 ways.

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