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### Lottery Permutations

```
Date: 5/16/96 at 18:47:34
Subject: Permutations

We am trying to determine the number of unique permutations of a
lottery where you pick 6 numbers out of 49, with numbers not allowed
to repeat.

Also, we are having some trouble determining the odds of picking the
winning set randomly.

Finally, we are having a heated discussion on how buying a large
number (unrealistically large), say 5,000,000 lotto tickets, would
affect your odds of picking the winning numbers.  Given a lotto that

```

```
Date: 6/14/96 at 19:7:49
From: Doctor Anthony
Subject: Re: Permutations

The number of possible combinations of 6 numbers selected from 49
(without repetition) is

49_C_6 = 13,983,816

So probability of a correct set is 1/(49_C_6)

If you bought 5 million tickets, then you would have 5 million chances
out of 14 million odds of having the winning ticket.  To give yourself
a probability of 1 of having a winning ticket, you would have to buy
~14 million.  Since many others might have the winning numbers as
well, you could end up sharing the prize, and so reduce very
considerably what you earn.  Against that, you would also be winning
all the possible lesser prizes of having 5 right numbers, 4 right
numbers, and so on with other tickets that you had bought.

marginally if the lesser prizes were generous, but your expectation
will always be highly negative.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Permutations and Combinations
High School Probability

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