In the california state lottery, you must select six numbers from fifty-two numbers to win the big prize. the numbers do not have to be in a particular order. what is the probability that you will win the big prize if you buy one ticket?

C (n, r) = [n! / ((n-r) !*r!) ]

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n is the number of possibilities and it is 52 in question and r is the number of

things to be taken at a time which is 6

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if we substitiue

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C (n, r) = [52! / ((52-6) !*6!) = 52! / ((46) !*6!) ]

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52! = 52*51*49*48*47*46*45*44*43*42 * ... and 46! = 46*45*44*43*42 * ...

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you divide 52! by 46! the result after canceling all the

common terms is just 52*51*50*49*48*47. The question is reduced 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.