# Tagged Questions

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

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### Circular permutation (no two are consecutive)

Find the number of ways of selecting 3 people out of N persons around a circle if no two of them are consecutive.
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### A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue? I am helpless regarding this. I don't know how to solve it....
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### how many different ways a set of ten variables could be ranked from highest to lowest value, given three possible integer values for each variable

I'm trying to solve a problem involving how many different ways a set of ten variables could be ranked from highest to lowest value, given three possible integer values for each variable. It's been ...
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### Solve $\max \mathrm{sum}(AXB \geq \gamma), X \in \{0,1\}^{N \times N}$

I have a problem to find the best permutation matrix $X \in \{0,1\}^{N \times N}$, so as to maximize the number of elements in $AXB$ which are above a certain positive number $\gamma$. In other ...
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### Why doesn't this alternative method work? Chance of getting four of a kind in a hand of $5$ cards?

Please note: This is not a duplicate since it is asking about an alternative method of solving the question What is the probability of getting four of a kind in a hand of $5$ cards from a standard ...
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### Suppose that an ice-cream café has 10 different flavors of ice cream. [closed]

In how many different ways one can choose 3 scoops of ice-cream, so that order of flavors does not matter?
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### In how many ways can an inspector visit $4$ normal sites and $1$ “suspicious” one?

I cannot figure out why my answer to the following question is wrong: Suppose that a weapons inspector must inspect each of five different sites twice, visiting one site per day. The inspector is ...
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### How many possible solutions are there in 4 number game?

$4$ number game consist of $4$ random number from $0$ to $9$. The goal is to make the result equal to $24$. There are only operation four operation possible, addition, subtraction, multiplication, and ...
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### Orbits of the permutation action of a subgroup on its cosets

Consider a finite group $G$ and a subgroup $H \subseteq G$. There is a transitive group action of $G$ on the set of left cosets $gH$ by left multiplication, and the stabilizer of $gH$ is $gHg^{-1}$. ...
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### Permutation/Combination Assistance

I'm stuck on the following permutation/combination problem... John won 10 tickets to the Falcons/Ravens game by calling into a radio station’s contest. Find the number of ways he can invite family ...
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### n points permuted on a circle

Here is a combinatorics problem that bothers me a lot. I am looking forward to a quick reply. Thanks in advance. Here goes the problem. Initially there are $n$ points on a circle. We do permutation to ...
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### Proof that a transitive permutation group (G, X) with G abelian, is sharply regular

As the title states, the question is the following: Let (G, X) be a transitive permutation group, where G is abelian. Show that (G, X) is "sharply regular". First of all I want to notice that in my ...
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### Limit of probability that a permutation of $\mathcal{S}_n$ has a $k$-cycle is $1 - e^{-1/k}$?

Choose a random permutation $\sigma \in \mathcal{S}_n$. What's the probability that it contains a $k$-cycle as you take $n \to \infty$? I ran a couple examples and it seems to approach $1 - e^{-1/k}$....
### Notation for probability: $C_n^r$, $P_n^r$, $A_n^r$?
I was told that $C^{n}_{k}$ refers to combinations or choose k elements from n elements, $\bar{C^{n}_{k}}$ refers to combinations with repetitions (i.e. $C^{n+k-1}_{k}$), and $P^{n}_{k}$ refers to ...