1. ### I Cardinality of Unions of Powersets

Mentor note: In this thread I (Mark44) have edited "cardinal" to "cardinality." In English, we talk about the "cardinality of a set," not the "cardinal of the set." Given A a set of n elements - note |A| its cardinal and P(A) its powerset. Let A1, A2... Ak, be k subsets (not empty) of A. What...
2. ### Rook polynomial

This is my solution however I feel like the number is far too big can anyone see what I’ve done wrong
3. ### Why Potential Energy cannot be included twice?

If for example I have two charged particles q_1 , q_2 with distance 'r' between them, then: The potential energy that results from particle q_1 exerting force on particle q_2 is $$k\frac{q_1 q_2}{r}$$ If I do the same process for particle q_2: The potential energy that results...
4. ### B Permutations and combinations

The total number of different combinations of one or more letters which can be made from the letters of the word MISSISSIPPI is? First i dont understand what the question means and second my answer is completely different from that in my book My working- since there are 11 letter 4 I 4 S 2 P...
5. S

### B Linear combinations

Hi, I read that linear combinations of a state, Psi, can be as: \begin{equation} \Psi = \alpha \psi + \beta \psi \end{equation} where ##\alpha## and ##\beta## are arbitrary constants. Can however this be a valid linear combination? \begin{equation} \Psi = \alpha \psi \times \beta \psi...
6. ### 8 balls how to arrange for adjoining?

Homework Statement Homework Equations The Attempt at a Solution the answer for no adjoining _W_W_W_W_W_ for 3 red balls, there are 6 positions so ## 6C_3 = 20## i'm curious, on other way to find arrangement? for adjoining = all arrangement - adjoining all arrangement = 3 red can get to...
7. ### 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...
8. ### 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...
9. ### How many ways can you arrange 52 things into 4 groups BUT th

How many ways can you arrange 52 things into 4 groups BUT the groups do not have to be the same size?!?
10. ### Ways to put letters in postboxes

Homework Statement There are 7 different postbox, and 10 identical letters. How many ways can the letters put into the boxes so that there is at least one letter in a postbox? Homework Equations nCr=n!/(n-r)!r! If M,N,O..... things can be done in m,n,o..... ways then ways of doing them...
11. ### 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...
12. ### Proving combination is a natural number by induction

Hi, I've seen on on several sites that you can prove that nCr, where r<=n, is a natural number. I'm not sure how to do this by induction. So I need help on this proof. How do I write this as a mathematical statement at the start of the induction proof? Thank you