5 checks and envelopes are addressed to 5 different people. The checks are randomly inserted in the envelopes.  What's the probability that exactly 3 checks are inserted in the correct envelopes?

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Yankee -If you are asked for a "probability", then you must calculate both the denominator and the numerator.  The denominator is the "total possible outcomes". The numerator is simply the number of outcomes that match the event.Let's work on the denominator first.  The total possible outcomes are as follows:5 ways to insert the first check4 ways to insert the second check3 ways to insert the third check2 ways to insert the fourth check1 way to insert the last checkThere are 5 factorial (5!) total possible outcomes or 5x4x3x2x1=120 = denominatorThe numerator is a little more complex.  If you place the 5 envelopes on a table and you know 3 have a correct check, then how many ways can you arrange the 3 correct matches?  If you write them all out, you will see that there are 10 ways.  That leaves the remaining two envelopes that must have no match.  There is only one way for that to happen.So the numerator = 10x1=10 ways.The final probability = 10/120 or 1/12Hope that helps