Solving a Probability Problem: Purchasing Defective TVs for a Hotel

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The problem involves calculating the number of ways a hotel can purchase 5 TVs from a shipment of 12, which includes 3 defective units. To receive at least 2 defective TVs, the hotel can either take all 3 defective sets with 2 working TVs or 2 defective sets with 3 working TVs. The calculations involve combinations of selecting the defective and working TVs from the total available. This approach allows for determining the total valid combinations that meet the criteria. The solution requires careful consideration of the different scenarios for selecting the TVs.
leright
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Any help would be appreciated. I just want a push in the right direction...I am kinda struggling with these problems.

A shipment of 12 TVs contains 3 defective sets. In how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets?

Thanks.
 
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Count the number of sets which can be written like so:

{all three defective TVs} \cup {a set containing precisely two working TVs}, or

{a set containing precisely two defective TVs} \cup {a set containing precisely three working TVs}.
 
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