SOLUTION: In a drawing of six numbers using the same balls numbered 0 to 9, what are the odds that the same number will be drawn twice?

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Question 588272: In a drawing of six numbers using the same balls numbered 0 to 9, what are the odds that the same number will be drawn twice?

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
In a drawing of six numbers using the same balls numbered 0 to 9, what are the
odds that the same number will be drawn twice?
The number of failures is the number of permutations of 9 things taken 6 at a
time, or P(9,6) = 9·8·7·6·5·4 = 60480

The number of possible sequences of 6 is 9·9·9·9·9·9 = 96

The number of successes is 96 - P(9,6) = 531441 - 60480 = 470961 

So The odds in favor = (number of successes):(number of failures) =

470961:60480

which reduces to 

17443:2240

or about 7.8 to 1

Edwin