SOLUTION: 2. What would be the probability that randomly choosing four states from the top 7 murder states would actually be the top 4 states for murders in the United States in exact correc

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Question 1119153: 2. What would be the probability that randomly choosing four states from the top 7 murder states would actually be the top 4 states for murders in the United States in exact correct decreasing order?
(1. CA, 2. TX, 3. PA, 4. NY) Simplify all fraction answers.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
By choosing randomly, you may have the list of 7*6*5*4 = 840 different lines,

containing the names of the 7 top states, written by four in each line.


Only ONE line represents the correct ordered set.


So, the probability under the question is  .

Solved.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


One nice thing about probability problems is that you can usually solve them by several different methods.

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.

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;

Then the probability of making all the right choices is
(1/7)(1/6)(1/5)(1/4) = 1/840.
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