Question 1119153
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One nice thing about probability problems is that you can usually solve them by several different methods.<br>
The solution by tutor @ikleyn shows (and explains) one method for this problem: there are 7*6*5*4 = 840 different orders in which you can choose 4 of the 7 states; only one of those orders has the top four in the right order, so the probability is 1/840.<br>
You can also look at solving the problem by considering the probability that each choice made is the correct choice:
The probability of choosing the right state for 1st place is 1/7;
the probability of choosing the right state for 2nd place is 1/6;
the probability of choosing the right state for 3rd place is 1/5;
the probability of choosing the right state for 4th place is 1/4;<br>
Then the probability of making all the right choices is
(1/7)(1/6)(1/5)(1/4) = 1/840.