You can
put this solution on YOUR website!The lack of having to draw the six winning numbers in any particular order makes this a combination
problem. And the equation for calculating a combination is:
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C(n,r) = [n!/((n-r)!*r!)]
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where n is the number of possibilities (in this problem that is 52) and r is the number of
things to be taken at a time (in this problem r is 6).
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Substituting the numbers from this problem results in:
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C(n,r) = [52!/((52-6)!*6!)= 52!/((46)!*6!)]
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But 52! = 52*51*49*48*47*46*45*44*43*42*..... and 46! = 46*45*44*43*42*....
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You may be able to see that if you divide 52! by 46! the result after canceling all the
common terms is just 52*51*50*49*48*47. This reduces the combination problem to:
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C(n,r) = (52*51*50*49*48*47)/6!
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and 6! = 6*5*4*3*2*1
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If you want you can divide the numbers from 6! into the numbers in the numerator to simplify
things a little or you can just take your calculator and multiply out the numerator and
then divide that answer by 720 which is what 6! equals.
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If you just multiply out the numerator your calculator should tell you that the answer is
1.46581344*10^10 and when you divide that by 720 you get 20,358,520. This means that for
every 20,358,520 lottery tickets sold there is likely to be 1 winner among them. Pretty slim
odds of your ticket being that one.
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If you have a cheap scientific calculator you might examine it carefully to see if it has
a key function labeled nCr. If you do it will calculate this combination automatically.
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Just enter 52, then press the nCr function, then enter 2, and press the equal sign.
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