SOLUTION: To win at LOTTO in one​ state, one must correctly select 4 numbers from a collection of 65 numbers​

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Question 1207209: To win at LOTTO in one​ state, one must correctly select 4 numbers from a collection of 65 numbers​
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

If you ask for the number of ways to select numbers from without regard to the order, where the order of selection does not matter, you need the combination formula:



where is the total number of items to choose from, is the number of items to choose

in your case, and



...cancel





Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
If your teacher won't let you use a calculator with combinations on it,
then you might like this formula better: 

the number of combinations of n things taken r at a time 

is



So, for C(65,4), we start with 65, then come down 1 each time until we
have 4 factors on top, matched by the 4 factors of 4! on the bottom:



Then the 4 cancels into the 64 giving 16, 
The 3 cancels into the 63 giving 21,
The 2 cancels into the 62 giving 31.

So the answer is (65)(16)(21)(31) = 677040

Edwin
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