# Questions tagged [permutations]

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

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### Number of ways of distributing 75 identical objects into 4 boxes such that each box contains at least 15 objects.

There are 75 distinguishable objects, to be distributed into 4 distinguishable boxes. In how many ways can they be distributed such that each box contain at least 15 objects. Is there way to solve ...
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### Probability - Choosing two numbers from {1,2,3,4,5,6} such that one is lesser than 4

Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4, is? The correct method to solve ...
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### NOT Every permutation can be expressed as the product transpositions

I read the following claim: Every permutation can be expressed as the product of one and only one of the following: an odd number of transpositions ⟺ odd permutation an even number of transpositions ⟺...
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### problem of combination and permutations.. I tried to make the problem a little more difficult.. can't verify whether answer of right or wrong

Four visitors A, B, C and D arrived at a town that has 5 hotels. In how many ways, can they disperse themselves among 5 hotels? Since it is not mentioned in the question that whether more than more ...
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### Is there a relation between principle of addition, principle of multiplication and mutually exclusive, independent events?

My understanding is as follows: (a) If we have two events that are independent, then we can directly apply the principle of multiplication (b) If we have two events that are mutually exclusive, then ...
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### The product of two odd permutations is even intuition [duplicate]

I dont understand why the product of two odd permutations is even. I tried searching on the internet but I did not find a good answer where I understand. Thus, I am asking for an intuitive ...
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### What is the connection between the notions of cyclic permutation and cyclic group?

I am working with the following definitions: If a permutation consists of exactly one cycle (that is, if the $m$ for which $\pi^m = id_X$ is equal to the cardinality of $X$, $m = n$) then we say that ...
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