As far as my understanding goes, it computes the number of ways you can give out n names to n people without any of them having their own name.

That is the number of derangements which is always an integer. Your sum there is not always an integer.

]]>Summation from j= 0 to n of (-1)^j/j! in the numerator is not getting into my head.

As far as my understanding goes, it computes the number of ways you can give out n names to n people without any of them having their own name.

Why do we need to multiply the summation in the numerator with P(no one getting drunk)?

]]>Now if you tell me what you are trying to do I can suggest a good means of computing the numbers.

]]>Although I do not understand the 2nd summation in the numerator. What does it compute? the probability that n people (who are gonna get drunk) don't have each other's name?]]>

Sorry, but the closed form is gigantic. Would a recurrence relation be okay?

]]>It is no bother.

J is what is called a dummy variable. It is an index of summation.

I can try to get a closed form for the whole expression.

]]>here is something slightly less complicated inasmuch as there is no gamma function.]]>

I used the idea of spotting the pattern. This is in the style of the new experimental mathematics or should I say the old.

We could then work on a method to prove the formula, say by induction.

Very often in combinatorics formulas and answers are found in this manner.

For your second question, that is the simplest form I know. What do you need explained?

]]>Hi;

If possible, can you please write this in a simplier format? as I don't quite understand these notations. Thank you very much.

]]>But to answer a) when stuck it is not a disgrace to list them all and do it by hand. Anything beats no answer!

Calling each person 1 to 5, the number of different ways to arrange them with no fixed points is called derangements. For 5 of anything there are 44 of them.

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