SOLUTION: Five lotto numbers are to be picked at random from a collection of 100 numbers. Order does not matter. How many combinations of lotto numbers are there?

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Question 313187: Five lotto numbers are to be picked at random from a collection of 100 numbers. Order does not matter. How many combinations of lotto numbers are there?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You need the number of ways to select things from a selection of things where order does not matter.





Which is some very nasty arithmetic. However, there is a shortcut...

If you divide by you get

Then divide this product by

The 5 goes into 100 20 times, the 4 goes into 96 24 times, the 3 goes into 99 33 times and the 2 goes into 98 49 times, so the whole thing reduces to:



Somewhat simpler. You can take it from here.

John