# Tagged Questions

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### count the permutation which have $k$ maxima

I need some help for the following homework question. A permutation $P (\pi_1\pi_2...\pi_n)$ of {$1,2,...,n$} is given. We say that $j$ is a maxima of $P$ whenever $\pi_j$>$j$. How can I find ...
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### Removing the Summation (Closed Form)

The following question from "Combinatorics of Permutations" : $$E[X] = \sum\limits_{k = 2}^n \frac{k\cdot T(n,k)}{n!}$$ where  T(n,k) = k \cdot T(n-1, k) + 2 \cdot T(n-1, k-1) + (n-k) \cdot ...
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### Recurrence relation question - check my answers! Basic questions.

I had a chat with a friend about these questions (they are homework questions) , and we argued about the solution. I would just like an outside opinion about my answers: 1) $n \geq 2$ people are ...
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### Recurrence relation - simple question. Homework. Permutations with a twist,

I think I solved it but I would love someone to tell me if I'm wrong. the question is as follows: $n$ people are sitting on a bench with $n$ seats. Find a recursive equation that calculates how many ...
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### number of derangements

In the normal derangement problem we have to count the number of derangement when each counter has just one correct house,what if some counters have shared houses. A derangement of n numbers is a ...
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### How is the algorithm for recursively printing permutations of a set of numbers this equation our professor gave us?

I'm having a great amount of trouble understanding where my prof got $T(m, n) = n(T(m+1, n-1) + m+1 + n)$ if $n > 1$ as the recursive formula for the algorithm for recursively printing the ...
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### all possible sequences of positive integers that sum upto N and are strictly increasing

I have $N$ bricks and i have to build a staircase. A staircase will consist of steps of different sizes in decreasing order, no two step size should be same. Each step should consists of atleast one ...
### Circular permutation of $k$ types of items on $n$ places with no two adjacent items of the same type. [duplicate]
Possible Duplicate: In how many ways we can put $r$ distinct objects into $n$ baskets? I have been trying to work out a problem but cannot get any closed formula or recurrence. You are ...
Given a set of $n$ mutually distinct elements, how many permutations are there such that exactly $k$ of the permuted elements stay at the same place? Example Let's take the set $\{A,B,C,D\}$. The ...