What is the probability of choosing 1st, 2nd, and 3rd place in a horse race fielding 12 horses?
We are assuming that every horse has an equally likely chance to win (or that you have no knowledge to the contrary.)
I. One method is this: the chance of selecting the first place finisher is 1/12; the chance of then selecting the second place finisher is 1/11 (as there are only 11 horses left to choose from since you selected first place correctly); and the probability of selecting the third place horse having already selected the first and second place horses is 1/10.
The probability of all three happening is 1/12*1/11*1/10=1/1320
II. Another method is to find the size of the sample space. Since order matters, we find the number of permutations of 12 items taken three at a time to be `_12P_3=1320` . As there is only one correct selection, the probability is 1/1320 as before.