SOLUTION: A shipment of 141 laptops contains 7 defective laptops. A quality control specialist chooses a sample of 8 laptops from the shipment. How many possible choices of 8 laptops can

(a)   How many possible choices of 8 laptops can be made?

       =  = 3165326793495.


      If it is boring to you to write so long formulas, you can use an Excel standard function combin(141,8).



(b)   How many of these possible selections will not contain any defective laptops?

       =  = 1959267085776.



(c)   How many of the possible selections will contain at least one defective laptop?

      This number is   -  = (a) - (b) = combin(141,8) - combin(133,8) = 3165326793495 - 1959267085776 = 1206059707719.



(d)    How many of the possible selections will contain exactly one defective laptop?

       . = 8*combin(133,7) = 8*124397910208 = 995183281664.