# Tagged Questions

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### Problematic Permutation Problem

i see a problem without any definition. would you please help me? i want to calculate the number of permutations of 1,2,...,1392 that 696 numbers be in the natural positions (from all numbers, 696 ...
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### Counting valid tickets

I think my question is very easy but I need to understand. The problem is, I have a ticket with 2 numbers from 1 to 10. The first number cannot be greather than the second number. How many valid ...
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### Determining the different number of subsets (counting, permutations, combinations)

Given that any fixed integer n>0, let S={1,2,3,4,...,n}. Now a Red-Blue subset of S is called T. Every element of T is given a colour (either red or blue). For instance {17 (red)}, {1 (red), 5(red)} ...
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### Permutations, Combinations, and Counting

A group of 63 people are camping together. They have two 6-person tents, three 4-person tents, five 3-person tents, and three 2 person tents. 18 people will sleep outside of the tents under a tarp. ...
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### Count Number of Sequences

The question is: Given a sequence of positive integers A={1,2,3,...,N}. Count the number of sequences you can get after making K swaps between adjacent element on it for a given N ? My approach: My ...
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### DNA Sequence Distinct Way

we know The genetic code is based on the four nucleotides adenine (A), cytosine (C), guanine (G), and thymine (T). These are connected in long strings to form DNA molecule. with three A, one C, two G ...
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### How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A?

As the title states, the question is: "How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A?" I don't really get what the problem ...
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### What does “order matters” regarding permutations refer to?

I psychoanalyze EVERYTHING and permutations/combinations are frustrating me. Sorry for posting so many questions lately but I really appreciate all of the help! Ok so I know the permutation formula: ...
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### Can someone please explain the reasoning for this permutation problem?

I'm studying and reading through my discrete math book.. I seemed to be grasping the idea of permutations, but I don't understand how the solution for this particular problem came to be. Question: ...
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### Can someone please clarify combinations vs permutations?

I see similar questions asked on here and obviously I did some research and read my book, but it seems like every explanation contradicts another in some way. There are basically infinite scenarios ...
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### What's the difference between a permutation and a combination with repetition?

My understanding is that a permutation is used to find the number of rearrangements of different elements, taking into account possible orders. A combination is used to find the number of ...
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### In how many ways can you arrange the alphabet so that A and B are always next to one another (In either order)

Ok, so I have no idea where to begin on this question. Do I treat A and B as one letter? 25 choose n?
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### How do I find “at most” x bit strings of length 20?

I tried searching online and I found several examples of doing such problems, but I'm still not sure if I'm doing them correctly and would greatly appreciate some help! How many bit strings of length ...
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### I want to generate(or count) all possible binary matrix that satisfy certain Condition

I want to generate(or count) all possible binary matrix that satisfy below Condition. let A be arbitrary binary matrix 4*4 ...
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### How many positive integers n can we make with the digits 3, 3, 4, 5, 5, 6, 7, if the number n > 4, 000, 000?

According to my study guide the answer to the exercise, How many positive integers, (n), can we make with the digits 3, 3, 4, 5, 5, 6, 7, if the number n > 4, 000, 000, : The total of numbers n > ...
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### How many different 5 characters words are there with only one letter a?

I just need to clarify my answer to this exercise. This is a permutations exercise. If we define a word to be a string of 5 letters of the English alphabet, regardless of meaning, then mnnnw is a ...
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### A bowl contains 10 red balls and 10 blue balls, A women selects ball at random without looking?

How can we solve this question ? A bowl contains $10$ red balls and $10$ blue balls, and a women picks up balls from the bowl, at random, without looking. A) How many balls must she pickup in ...
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### Using Binomial Theorem to show that (-1)^k C(n,k) [duplicate]

I came across this question on my text book and i didn't know how to prove it. Use the Binomial Theorem to show that $$0=\sum_{k=0}^n \ (-1)^ {k} C(n,k)$$
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### Give a combinatorial argument to show that C(n,k) = C(n,n-k)

What is combinatorial argument and how can i prove this equation ? As far i understand i think we have to apply the Chu-Vandermonde identity but i am not sure if thats right or not. ...
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### Expected Value of Local Maxima and Local Minima

Recently I came across this question: Given a random permutation of integers 1, 2, 3, …, n with a discrete, uniform distribution, find the expected number of local maxima. (A number is a local maxima ...
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### Ways to select three-man teams

In a competition there are 18 competitors. Answer the following: A) During the first day they're competing in three-man teams (total of 6 teams). How many ways are there to select the teams? B) If ...
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### combination and permutation !!!!

I have 3 questions that i had a try to do but i didn't understand them could anybody please help me to solve these questions. For Q1 i know how to use the multiplication counting procedures for a) i ...
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### proving bitstrings [duplicate]

1.Let it be $a_n$ the number of bitstrings which contain 000 How would I prove that for $n\ge4$: $$a_n = a_{(n-1)} + a_{(n-2)} + a_{(n-3)} + 2^{n-3}$$
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### Calculate product of transpositions

I've searched for this kind of question-answer, but didn't managed to find one because the problem is quite specific. Let me explain: I have permutation: $(13927)(5846)$ which I must write as ...
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### Number of orders and combinations

I have just done these two questions and I have answers for them but I am not sure if they are correct. A jazz band is to give one concert in each of nine selected cities. Calculate the total ...
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### Permutations of word 'mathematics'

How many arrangements are there of MATHEMATICS with both T's before both A's or both A's before both M's or both M's before the E ? Can someone also point to some online resource that has such ...
A professor asks a true/false question with ten individual questions. Suppose the professor assigns grades of: $10$ points for each correct response, $0$ points for each absent response, and $-10$ for ...