How Do You Calculate Samples Containing Defective Widgets?

[liahow]

I am working on a problem in which there are 100 widgets. I need to find how many samples of size 5 there are, which I found to be 75,287,520. No problem there. I am not sure how to go about the next part, however. In the original set of 100 widgets, 3 are broken. How many of the samples of 5 contain at least one of these broken widgets? No idea how to do that. Can someone please help? Thanks!

 

[mathman]

The probability that a given set of 5 widgets has no broken ones is
(97*96*95*94*93)/(100*99*98*97*96). Multiply that by the total number of combinations to get the number without any broken.

 

[mathman]

If you want to use the basic counting formula, remove the 3 bad widgets from the set and you have 97. Calculate the number of samples of size 5 for the 97 and subtract from the number of samples of 5 for 100.