Suppose that 40 batteries are shipped to an auto parts store, and that 4 of those are defective. a fleet manager then buys 8 of the batteries from the store. in how many ways can at least 3 defective batteries be included in the purchase?

From the given above, we will include the case in which 3 and all 4 defectives are included in the purchase. 

For 3:
                       (36C5) x (4C3) = 1507968
For 4:
                       (36C4) x (4C4) = 58905
Adding these numbers will give us an answer of 1566873.