2011-11-07, 04:09 PM
The chance that all twenty car plates will be different is:
100!/((100 - 20)! * (100^20)) = 13,04%
Or the complementary, the chance that at least one plate will be the same is 86,96%
So the odds are extremely against the guy betting they'll all be different (even a 1:5 bet is disadvantageous).
Not gonna calculate the expected value here, it's not hard though.
For a group of N possibilities, the chance that in n different picks all will be different is:
N!/((N - n)! * N^n))
100!/((100 - 20)! * (100^20)) = 13,04%
Or the complementary, the chance that at least one plate will be the same is 86,96%
So the odds are extremely against the guy betting they'll all be different (even a 1:5 bet is disadvantageous).
Not gonna calculate the expected value here, it's not hard though.
For a group of N possibilities, the chance that in n different picks all will be different is:
N!/((N - n)! * N^n))