combinatorics

Straight Variant: The only difference is that the top rank can bridge the 1st rank to form a sequence. Think of it as if Q, K, A, 2, 3 was a legal straight. How is that calculated? A More Complex Straight Variant: This one gets trickier, I think. In this variant, there are: 64 cards 4 suits 13...

Consider a hypothetical example. There are 12 tickets for a documentary film and exactly 12 people to buy the tickets (one person can buy only one ticket). There are 3 ticketbooths for selling the tickets and each ticketbooth will sell exactly 4 tickets. Suppose the researcher labels the 12...

I have an SPSS data set with 500+ respondents and 18 symptoms that they could have. Each symptom has its own variable Symptom01 = 1 means they have the symptom 1 Symptom02 = 0 means they dont have the symptom 2 etc etc What I want to know is what combination of 3 symptoms is more frequent...

There are 100 U.S Senators, two from each of the 50 States. If 12 Senators are randomly chosen to form a committee, what is the probabilty that they are alll from different states? If 12 senators are chosen at random from the 100 senators, what is the probabilty that neither of the two...

Design: For 18 trials numbers (either 0 or 1) are randomly selected, a random portion of the first 9 are 0 and the last 9 are set as the opposite number of 0s. Within the first and last 9 the 0 or 1s are randomly assorted. The numbers are described as being in 3 consecutive groups of 6 called...

Every year, 6 Irish families, represented by 4 members each, meet up and rent 3 minivans of 8 seats each to go to a big festival. In order to mix things up a little, each individual selects a random car, i.e. family members don’t deliberately try to be in the same car, although they might by...

A teenage girl wants to select a 5-digit pin for her social network account. How many different possible pin #'s are there if. (a) digits can repeat (b) digits cant be repeated I'm trying to research how to solve but I'm not sure if this is a combo or permutation question. If...

Hi there, I have the following problem: Participants in my experiment were presented with 4 objects and 4 categories and asked to map each of the items to its correct category. It was a forced choice, so one and only one item could be mapped to each of the four category bins. I'd now like...

Suppose there are T buckets in a room. Suppose further that there are two individuals, 1 and 2, who each have B1 and B2 tennis balls, where B1 and B2 are smaller than or equal to T, but not necessarily equal. Now suppose that person 1 and 2 must throw their tennis balls into buckets. They...

Hi, Got the following question, I'm sure it's pretty simple but can't get to a solution :( There's a monthly employment survey, conducted by interviewing a sample of 21,500 people, out of a population of 5,800,000 people. What is the probability that 50 (assume random) people have not...

Given n buckets, each bucket containing m items, we want to select k items. Selecting an item means that the corresponding bucket is selected too. Question: How many buckets will be selected in the average case? What is the probability of selecting x buckets? (Items in the selection can...

Hi, I am trying to generate new variables in a stata dataset which includes all pairwise and triplets combinations of a count of 14 conditions. The conditions are listed as values in one variable 'chrondis' 1 to 14. chrondis | Freq. Percent Cum...