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

Algebra ->  Permutations -> SOLUTION: To win at LOTTO in one​ state, one must correctly select 4 numbers from a collection of 65 numbers​      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

If you ask for the number of ways to select 4 numbers from 65 without regard to the order, where the order of selection does not matter, you need the combination formula:

C%28n%2C+k%29+=+n%21%2F%28k%21%2A%28n-k%29%21%29

where+n is the total number of items to choose from, k+is the number of items to choose

in your case, n+=+65 and k+=+4

C%2865%2C+4%29+=+65%21%2F%284%21%2A%2865-4%29%21%29
C%2865%2C+4%29+=+65%21%2F%284%21%2A61%21%29
C%2865%2C+4%29+=%28%2865%2A64%2A63%2A62%29%2A61%21%29%2F%284%21%2A61%21%29...cancel 61%21
C%2865%2C+4%29+=%2865%2A64%2A63%2A62%29%2F%284%2A3%2A2%29
C%2865%2C+4%29+=+677040



Answer by Edwin McCravy(20054) About Me  (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

C%28n%2Cr%29%22=%22%22

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:

C%2865%2C4%29%22%22=%22%22%2865%2A64%2A63%2A62%29%2F%284%2A3%2A2%2A1%29%29

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