 # Get help with probability and combinatorics

Recent questions in Probability and combinatorics Andy Erickson 2022-05-23 Answered

### For any even $n$, say $n=2m$, a row complete Latin square of order $n$ can be formed by writing down$0,1,2m-1,2,2m-2,3,\dots ,m+1,m$as the first row and then developing subsequent rows by adding $1$ modulo $n$.I'm not quite clear on how that goes, such as what the difference is between $2m$ and $m$. $2m$ stands for $n$, does $m$ stand for modulo? I'd like to see and example with an even number or two, such as $4$, and $6$.I tried, $2m=4$$0,1,3,2,2\dots$wait, that can't be right. Erick Clay 2022-05-22 Answered

### Let's say, I have 4 yellow and 5 blue balls. How do I calculate in how many different orders I can place them? And what if I also have 3 red balls? Simone Werner 2022-05-22 Answered

### How can we show that the number of pairs $\left(a,b\right)$ (where the pairs $\left(a,b\right)$ and $\left(b,a\right)$ are considered same) with $\mathrm{lcm}\left(a,b\right)=n$ is equal to$\frac{\left(2{e}_{1}+1\right)\left(2{e}_{2}+1\right)...\left(2{e}_{k}+1\right)+1}{2},$Where$n={p}_{1}^{{e}_{1}}{p}_{2}^{{e}_{2}}\dots {p}_{k}^{{e}_{k}}$, pis are prime for all $1\le i\le k$. Angel Malone 2022-05-21 Answered

### What is the probability that a bridge hand will contain 13 cards of the same suit? zato1kom7 2022-05-21 Answered

### How many ways are there to color faces of a cube with N colors if two colorings are the same if it's possible to rotate the cube such that one coloring goes to another? Yasmin Camacho 2022-05-21 Answered

### Consider a deck of 52 cards (there are 13 cards of each suit).a. How many different ways can you arrange, in a line, the 13 cards of the suit of diamonds, so that the cards 7,8,9 and 10 stay together either in the beginning or the end of the line?b. 8 cards are extracted from the deck. What is the probability there is an ace and at least 3 queens in the extracted cards?Is there any method to solve probability questions?What strategies/lines of though do you use when tackling this kind of problems?Could you solve these problems using a method or several strategies and describe them?Is there any single method you can use to solve both of these seemingly different problems? copafumpv 2022-05-21 Answered

### Define a matching problem to be the following:1) n numbered boxes and n numbered cards2) you have to place all the cards. No empty boxes and no left behind cards are allowed.So you end up with a permutation of length n. The number of possible permutations being n!Let X be the variable of x matching places in an ordering.Only 1 permutation is correct. So $P\left(X=n\right)=\frac{1}{n!}$I would like to calculate $P\left(X=2\right)$, $P\left(X=3\right)$ and so on.$P\left(X=1\right)=0$ obviously... tilfaen4a 2022-05-21 Answered

### Lets assume we have a box with 45 coupons labeled 1-45. Now in this case I would like to adjust the CCP such that I can calculate the expected value (amount of draws necessary) to collect 10 specific items. For example item 1-10. How do I adjust my model such that I can calculate the amount of draws necessary to collect each item n times. copafumpv 2022-05-21 Answered

### Suppose that I am buying cakes for a party. There are $k$ different types and I intend to buy a total of $n$ cakes. How many different combinations of cakes could I possibly bring to the party? Despiniosnt 2022-05-21 Answered

### A manager must form a team of 5 from among 5 employees from group A and 6 employees from group B. If all employees have an equal chance of being selected, what is the approximate probability that a randomly selected group of 5 will consist of 2 employees from group A and 3 employees from group B? Jordyn Calhoun 2022-05-20 Answered

### We have at our disposal the following: the three letters a,b,c , and the five digits 1,2,3,4,5 . We have to form with them all the possible passwords of six (6) characters, under the condition that there must be at least one letter and at least one number in each password. Other than this there are no more restrictions (and, thus, one can repeat at will numbers, letters and etc.) Riley Yates 2022-05-20 Answered

### Evaluate $\sum _{k\ge 0}\left(-1{\right)}^{k}{\left(\genfrac{}{}{0}{}{n}{k}\right)}^{2}$ using sign reversing involutions. When $n$ is odd, the problem is trivial : let $\left[n\right]=\left\{1,2,\dots ,n\right\}$ consider all pairs of subsets $\left\{\left(A,B\right)\in {2}^{\left[n\right]}×{2}^{\left[n\right]}:|A|=|B|\right\}$, and $\left(A,B\right)$ has sign $\left(-1{\right)}^{|A|}$ and the sign-reversing involution is $\left(A,B\right)\to \left(\left[n\right]-A,\left[n\right]-B\right)$. Any hints on how to approach this problem for even $n$ will be appreciated. qtbabe9876a9 2022-05-19 Answered

### My idea is that by finding the combination of arranging the 10 bears into the sample, this can be used to calculate the probability. For example, this would be ${}_{10}{C}_{5}=30240$. However, how would I calculate the number of arrangements of the four bears that will go into the sample? I considered ${}_{5}{C}_{4}$, yet this would be illogical as it only includes the number of arrangements of the four bears in the sample, but does not consider the arrangements in the sample not selected. Is my working correct? adocidasiaqxm 2022-05-17 Answered

### Probability of getting a sum of 14 when rolling 11 dice.I assume that in P(A) = m/n, n is 6^11, but I don't know how to calculate the number of ways to get a sum of 14 when rolling 11 dice. mars6svhym 2022-05-16 Answered

### Factorial is defined as$n!=n\left(n-1\right)\left(n-2\right)\cdots 1$But why mathematicians named this thing as factorial? Brody Collins 2022-05-15 Answered

### How does the Glivenko-Cantelli theorem improve the stochastic convergence of the empirical distribution ${F}_{n}\left(x\right)$?Let ${X}_{i}$ be iid random variables with empirical cumulative distribution function ${F}_{n}\left(x\right)$ and CDF $F\left(x\right)$. From the central limit theorem and the strong law of large numbers, we know that ${F}_{n}\stackrel{d/a.s.}{\to }F$ . The Glivenko-Cantelli theorem states that $\underset{x\in \mathbb{R}}{sup}|{F}_{n}\left(x\right)-F\left(x\right)|\to 0$ almost surely. How does it impact improvements for these two types of convergence (by itself or maybe by other theorems that are implied)? rynosluv101wopds 2022-05-15 Answered

### Let's say that I have two ordered sets of numbers $\left\{1,2\right\}$ and $\left\{3,4\right\}$. I'm trying to figure out the number of possible ways to combine these two sets into one without breaking the ordering of the two sets.So for instance, $\left\{1,2,3,4\right\}$, $\left\{3,4,1,2\right\}$, and $\left\{1,3,2,4\right\}$ are valid combinations, but $\left\{2,1,4,3\right\}$ isn't. How do I figure out the number of valid combinations? This feels like something I should remember from college, but I'm drawing a blank. It feels somewhere in between a combination and a permutation. Sappeycuii 2022-05-14 Answered

### given a multiset (a set with repetitions allowed) of $2n+1$ real numbers, say $S=\left\{{r}_{1},\dots ,{r}_{2n+1}\right\}$. These numbers are such that for every $k$, the multiset $S-\left\{{r}_{k}\right\}$ can be split into two multisets of size $n$ each, such that the sum of numbers in one multiset is same as the sum of numbers in the other.Show that all the numbers must be equal.( i.e. ${r}_{i}={r}_{j}$) Oberhangaps5z 2022-05-13 Answered

### A large white cube is painted red, and then cut into 27 identical smaller cubes. These smaller cubes are shuffled randomly.A blind man (who also cannot feel the paint) reassembles the small cubes into a large one. What is the probability that the outside of this large cube is completely red? Iyana Macdonald 2022-05-12 Answered

### We have 3 that qualify as best three, say BBB, and 2 as bad say OO.Thus, the total outcomes can be calculated as follows: 0 bad : This will be 1 as only one way to choose the best three 1 bad : This will be 3 ways. 'OBB' is one example and can be arranged in 3 ways. 2 bad : 3 ways.Thus, the total outcomes according to me should be 7, not 10. What am I doing wrong?

Even though it is always placed into the field of Precalculus, probability and combinatorics problems are more related to analytics and statistical information that many students implement as they are working with the accuracy of their research data. It is one of the reasons why finding good probability combinatorics examples is both complex and not. It is good to have a look through probability combinatorics questions as these will provide you with the answers and help understand how equations work and why possible outcomes are vital for understanding how the calculation takes place.