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...
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...
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...
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...
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...
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...
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...
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...
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...
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