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
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