SOLUTION: 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 or

Algebra.Com
Question 85849: 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

Found 2 solutions by checkley75, Edwin McCravy:
Answer by checkley75(3666)   (Show Source): You can put this solution on YOUR website!
TO CHOICES FOR SELECTING THE FIRST NUMBER IS 49.
THE SECOND IS 48 CHOICES.
THE THIRD IS 47 CHOICES.
THE FOURTH IS 46 CHOICES.
ETC.
THUS WE HAVE:
49*48*47*46*45*44~1.0068347*10^10 COMBINATIONS OF NUMBERS.

Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
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


Checkley'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   <-- start with 49, get 6 factors coming down)
C(49,6) = ———————————————————   
              1·2·3·4·5·6      <-- start with 1, get 6 factors going up

Start cancelling.  Cancel the 6 in the bottom into the 48 in the top

               8
           49·48·47·46·45·44  
C(49,6) = ———————————————————   
              1·2·3·4·5·6    
                        1

Cancel the 5 in the bottom into the 45 in the top


               8        9
           49·48·47·46·45·44  
C(49,6) = ———————————————————   
              1·2·3·4·5·6    
                      1 1
  
Cancel the 4 in the bottom into the 44 in the top


               8        9 11
           49·48·47·46·45·44  
C(49,6) = ———————————————————   
              1·2·3·4·5·6    
                    1 1 1

Cancel the 3 in the bottom into the 9 in the top

 
                        3
               8        9 11
           49·48·47·46·45·44  
C(49,6) = ———————————————————   
              1·2·3·4·5·6    
                  1 1 1 1

Cancel the 2 in the bottom into the 8 in the top

 
               4        3
               8        9 11
           49·48·47·46·45·44  
C(49,6) = ———————————————————   
              1·2·3·4·5·6    
                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

RELATED QUESTIONS

to win a lotto in one state, one must correctly select 6 numbers from a collection of 46... (answered by Maths68)
To win at LOTTO in one​ state, one must correctly select 4 numbers from a collection of (answered by MathLover1,Edwin McCravy)
to win at LOTTO in one state,one must correctly select 4 numbers from a collection of 45... (answered by jim_thompson5910)
to win the lotto in one state, one must correctly select 8 numbers from a collection of... (answered by jorel1380)
to win at LOTTO in one state, one must correctly select 4 numbers from a collection of 61 (answered by checkley77)
To win at LOTTO in one​ state, one must correctly select 4 numbers from a collection of (answered by josmiceli,Edwin McCravy,ikleyn)
To win at LOTTO in one​ state, one must correctly select 4 numbers from a collection of (answered by ikleyn)
i dont understand how to (9) which of the following has the same vale as -2(-7) or how to (answered by checkley71)
To win the lottery in a certain state you must correctly select 6 distinct numbers from a (answered by Alan3354)