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September 18, 2015
Q. Big numbers can be lots of fun, so where's the fun in this one: You're playing a popular lottery game of choosing six random numbers from a set of 49, trying to match all the numbers in the drawing. How might you picture your possibilities here?
A. You start by figuring the number of ways of picking the six numbers as 49 x 48 x 47 x 46 x 45 x 44, then separate out the repetitions of your six selections by dividing by 6 x 5 x 4 x 3 x 2 x 1. Result: Your chance of winning is 1 out of 13,983,816, or about 1 in 14 million, say Alfred Posamentier and Bernd Thaller in “Numbers: Their Tales, Types, and Treasures.” “In order to visualize that probability (improbability?), imagine a chain of domino tiles on the roadside, stretching from New York City to Niagara Falls..., about 400 miles, with each domino measuring a bit under two inches, so the entire chain is about 14 million tiles.”
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