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### Probability (Permutation Combination)

Homework Statement There are 22 students in a class. The professor will divide the class into 4 groups. Group 1 and 2 have 5 members each whilst Group 3 and 4 have 6. Given that the teacher forms the group at random, find the probabilities of : A = event where Paula, Trina, Gia all belong in...
2. ### How many ways can 12 balls be arranged into 4 different rows

Homework Statement In how many ways can 12 balls be arranged into 4 different rows with each row having at least one ball (a) if the balls are identical? (b) if there are 6 identical red balls and 6 identical blue balls? Homework Equations The Attempt at a Solution a) Put 4 balls in each...
3. ### Need help with counting problems

Homework Statement Counting problems are a very tough subject to me, so if someone could give me tips, examples explaining what's really happening, that would be great. Homework Equations I know what permutations, variations, combinations, ... are. The problems involving only one of those...
4. ### I How many combinations of unique arrangements are there?

If there was a 1 billion x 1 billion x 1 billion cube made of 3D pixel cubes, and half of them are black and half of them are clear/colorless, then how many combinations of unique pixel arrangements are there? Would the amount of shapes/objects in this cube be infinite? (Assuming the black...
5. ### A Problem with Permutations

Hey guys , Could anyone here tell me the easiest way to solve for n , nP7 = 604800 , the traditional way (I'm currently using) is to divide 604800 by 10 and then 9 and so on until I get 1 as a result of that division , The problem is this way isn't helpful with all permutations I have in my...
6. ### Algorithm for creating unique groups of elements

Homework Statement so for a side task I'm supposed to assign people to groups for an icebreaker in python, can anyone give me links to theories that I could read up on or give me suggestion X number of people at my company signed up for a dinner roulette as a way to meet new people. Everyone...