# Probability Puzzle

1. Sep 9, 2010

### Raybert

On average, how many times do you need to roll six dice together to see all six different numbers turn up within a single such group roll?

2. Sep 9, 2010

### CompuChip

64.8 times?

3. Sep 13, 2010

### regor60

I agree, except for the .8 :)

4. Sep 13, 2010

### Jonathan Scott

I agreed with 64.8, for the following reasons:

There are 6! ways of throwing all six values and 66 possible results, so the probability in each throw is 6!/66 = (1*2*3*4*5*6)/(6*6*6*6*6*6) = (4*5)/(6*6*6*6) = 5/(3*3*6*6) = 5/324.

The average interval between such throws (or, as in this case, before the first such throw) is therefore the reciprocal of this, 324/5 = 64.8, as usual for a Poisson distribution.