# permutations

1. ### Coin Tossing Problems...

Hi Everyone, New to the forum. Terrible at math. I'm enrolled in a college Math 100 course, and I'm having some trouble understanding some concepts related to combinations, permutations, Pascal's Triangle, etc. Here are the problems I'm stuck on: Suppose 9 fair coins are tossed. Find the...
2. ### Combinatorics. What is this called?

Hi. I hope this is the right forum. Here's what I did: I took all the permutations of 1234 and arranged them based on how much the digits of any group of permutations are spread out. In every group, the next permutation is obtained by increasing every digit of the previous one by 1 (4 loops...
3. ### Permutation problems (circular & with repetition)

Suppose we have 3 A's, 5 B's, 7 C's, 9 D's, and one E, F, G, and H. 1. How many different arrangements of these letters are possible if I write them as a string? I believe this is 28! / (3! 5! 7! 9!). Seems pretty simple. 2. If I write my "string" as a loop, either around in a circle or...
4. ### R-Permutation Help

Suppose there are a group of 20 people. We must choose a president, vice-president, secretary, and treasurer. How many different such assignments are possible? I came up with P(20,4) = (20!/16!) = (20*19*18*17*16!/16!) = 20*19*18*17 The question I have is what is the difference between that...
5. ### Permutations questions

I am stuck on this problem: A bag contains 24 marbles: 4 purple, 12 blue, and 8 grey. How many ways can 5 marbles be drawn with all 5 marbles blue? Common sense tells me that there is only 1 way to pull 5 marbles and have all them be blue. I put the numbers into a formula and got 792...
6. ### A question about permutations..

Hi guys. I encountered an exercise on our Discrete Math class which asks the question: and the answer on the answer key is: . I just wonder, how come it is computed only as 15*14*13, wherein the solution is 15!/10! ? Isn't it supposed to be 15*14*13*12*11? Thanks in advance for your help!
7. ### Permutations and Combinations. I need help.

QUESTION: The letters of the word POSSESSES are written on nine cards, one on each card. The cards are shuffled and four of them are selected and arranged in a straight line. a. How many possible selections are there of four letters? b. How many arrangements are there of four letters? // I...
8. ### number of even/odd permutations is the same

Hi, I'm having trouble understanding the proof of why number of even and odd permutations in any group of permutations is always the same. (ie. half the permutations are even). The proof I've read uses mapping $\sigma \rightarrow (1,2) \sigma$ and remarks that it's a bijection. I understand...
9. ### Question regarding Permutations and Combinations.

Hi, I've been doing some Permutations and Combinations worksheets to study for an upcoming test however I'm stump on what I did wrong on a question. The question/answer I got is; People told me the answer is wrong, however I have no idea what I did wrong / what would be the correct way to...
10. ### Galaxy permutations & combinations

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11. ### indecomposable permutations

we say the permutation σ=a1…an∈Sn is indecomposable if a1,…aj≠[j],∀j<n. let f(n) be the count of the indecomposable permutations in Sn. show: i) ∑nj=1f(j)(n−j)!=n! and n≥1 ii) (∑n≥=1f(n)tn)(∑n≥=0n!tn)=(∑n≥=1n!tn)−1 to i) let Ai be the set of all perms σ∈Sn with σ[i]=[i] and σ∈Sn with σ[j]≠[j]...
12. ### How to evaluate total numbers lying between two in a set of linear permutations

I am trying to evaluate the total numbers which are lying between 20450757870 & 87500752074 when all the 11-digit significant numbers, formed by permuting the digits 0, 0, 0, 2, 4, 5, 5, 7, 7, 7, 8 together, are arranged in decreasing order. your help is highly appreciated. thanks...
13. ### combinations and permutations

Mathematical Linear Equations help in solving various tough combinations and permutations Arkansas vs Kentucky Live Stream AMA SuperCross 2015 Live Stream UFC 184 Live Stream Syracuse vs Duke Live Stream Arizona vs Utah Live Stream Texas vs Kansas Live Stream England vs Sri Lanka Live Stream...
14. ### Permutations

A bag contains 2 white balls,3 black balls and 4 red balls. How many permutations of 3 balls be drawn form the bag, if at least one black ball is to be included? I did this question and worked out that there are 19 possibilities from the drawers point of view but these cannot be used for...
15. ### Could some possibly list all combinations or permutations (unsure)

I'm unsure which one I'm looking for either combinations or permutations, I'm unsure of the correct definition. Basically I was hoping if one of you kind users could post all the different ways these letters could be set out in rows of 5, the letters are "H" "D" "A" for example HHHHH HHHHA...
16. ### permutations

View image: Resim I can't get the answer.It is 23 but I got 25.
17. ### permutations

With the letters of the word MATEMATIK, how many 9 lettered words can be(meaningfull or meaningless) written starting and ending with a vowel? My answer is 7.7!/2.2 but it seems to be wrong.
18. ### Permutations

1. How many cyclic permutations are there of set with n elements 2. Permutation \pi e S_{n} has k cycles of powers c_{1}..c_{k} show that: a) sgn(\pi)=\prod^{k}_{i=1} (-1)^{c_{i}-1} b) sgn(\pi)=(-1)^{n-k} for 1.. isn't it just simply n! if the cyclic permutation is defined as one with just 1...
19. ### derangements and permutations in cryptography

hi, i have a problem that i am having a bit of trouble with; we are given a partial key (missing 11 letters) for a mono-alphabetic substitution cipher and asked to calculate the number of possible keys given that no plaintext letter can be mapped to itself. ordinarily, the number of...
20. ### Simple Permutations and Combinations Problem

I quote a simple question as follows but having trouble getting to the suggested answer, kinda boring: Need help on that, Thanks. (Nod)