<PRE><B>Question 85849</B>
&lt;pre&gt;
Please throughly explain how to solve this problem: 
To win the Lotto in the state of Alabama, one must correctly select 6 numbers
from a collection of 49 (1 through 49). This order in which the selection is
made does not matter. How many different selections are possible? 
Thanks
&lt;font size = 3&gt;&lt;b&gt;

Checkley&#39;s answer is wrong. Since order does not matter, the answer will be 
the number of COMBINATIONS of 49 things taken 6 at a time:

           49╖48╖47╖46╖45╖44   &lt;-- start with 49, get 6 factors coming down)
C(49,6) = ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ   
              1╖2╖3╖4╖5╖6      &lt;-- start with 1, get 6 factors going up

Start cancelling.  Cancel the 6 in the bottom into the 48 in the top

               8
           49╖&lt;s&gt;48&lt;/s&gt;╖47╖46╖45╖44  
C(49,6) = ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ   
              1╖2╖3╖4╖5╖&lt;s&gt;6&lt;/s&gt;    
                        1

Cancel the 5 in the bottom into the 45 in the top


               8        9
           49╖&lt;s&gt;48&lt;/s&gt;╖47╖46╖&lt;s&gt;45&lt;/s&gt;╖44  
C(49,6) = ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ   
              1╖2╖3╖4╖&lt;s&gt;5&lt;/s&gt;╖&lt;s&gt;6&lt;/s&gt;    
                      1 1
  
Cancel the 4 in the bottom into the 44 in the top


               8        9 11
           49╖&lt;s&gt;48&lt;/s&gt;╖47╖46╖&lt;s&gt;45&lt;/s&gt;╖&lt;s&gt;44&lt;/s&gt;  
C(49,6) = ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ   
              1╖2╖3╖&lt;s&gt;4&lt;/s&gt;╖&lt;s&gt;5&lt;/s&gt;╖&lt;s&gt;6&lt;/s&gt;    
                    1 1 1

Cancel the 3 in the bottom into the 9 in the top

 
                        3
               8        &lt;s&gt;9&lt;/s&gt; 11
           49╖&lt;s&gt;48&lt;/s&gt;╖47╖46╖&lt;s&gt;45&lt;/s&gt;╖&lt;s&gt;44&lt;/s&gt;  
C(49,6) = ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ   
              1╖2╖&lt;s&gt;3&lt;/s&gt;╖&lt;s&gt;4&lt;/s&gt;╖&lt;s&gt;5&lt;/s&gt;╖&lt;s&gt;6&lt;/s&gt;    
                  1 1 1 1

Cancel the 2 in the bottom into the 8 in the top

 
               4        3
               &lt;s&gt;8&lt;/s&gt;        &lt;s&gt;9&lt;/s&gt; 11
           49╖&lt;s&gt;48&lt;/s&gt;╖47╖46╖&lt;s&gt;45&lt;/s&gt;╖&lt;s&gt;44&lt;/s&gt;  
C(49,6) = ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ   
              1╖&lt;s&gt;2&lt;/s&gt;╖&lt;s&gt;3&lt;/s&gt;╖&lt;s&gt;4&lt;/s&gt;╖&lt;s&gt;5&lt;/s&gt;╖&lt;s&gt;6&lt;/s&gt;    
                1 1 1 1 1

So we end up with

C(49,6) = 49╖4╖47╖46╖3╖11 = 13,983,816

(So you have 1 chance out of nearly 14 million of getting them all.
You can be sure the lotto creators have done this math!)

Edwin&lt;/pre&gt;</PRE>