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The Arithmetic of Winning at Lotto

September 11, 1988

The letter by Don Payne of Anaheim (Sept. 4) discussing "The Odds in Lotto" was wrong in its statement of how odds are calculated.

In lotto, a number cannot be used twice or more, as occurs in the method proposed by Payne. The actual number of combinations of 49 numbers taken 6 at a time, as in lotto is:

C = 49! = 13,983,816


The symbol ! designates a factorial number--one obtained by multiplying the indicated number by the product of all the positive whole numbers less than itself. Thus 6! = 654321 = 720.

Even though the real odds of 13.9 million to 1 for a lotto winner is almost a thousand times better than Payne's 13.8 billion, to me, it still seems to be pretty much of a long shot, no matter how big the pot.



The Times received 15 letters in response to Don Payne's calculations. All but one agreed that the winning Lotto odds are one in 13,983,816.

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