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) (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.
\ =\ \frac{n!}{k!(n\,-\,k)!})
\ =\ \frac{100!}{5!(100\,-\,5)!})
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
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