Permutations, combinations, bijective proofs, generating functions
0
votes
1answer
17 views
Elementary Probability and Statistics
A password consists of four letters followed by a three digit number.
How many passwords are possible if there are not restrictions?
4
votes
0answers
24 views
On the number of complete and gap-free compositions
This is a longish post about something that has been haunting me for a while about a kind of restricted composition, namely gap-free and complete compositions. First, I will define the terms that are ...
2
votes
2answers
24 views
Boston Celtics VS. LA Lakers- Expectation of series of games?
Boston celtics & LA Lakers play a series of games. the first team who win 4 games, win the whole series.
The probability of win or lose game is equal (1/2)
a. what is the ...
1
vote
2answers
28 views
How to get all combinations forms of 4 zeros out of 9 ones?
I have 9 digits, I need to figure out the 126 possibilities of 4 zeros out of 9 digits of number one.
Example:
...
0
votes
0answers
32 views
Question based on counting. [duplicate]
Given two integers $N$ and $M$, find how many permutations of $1, 2, ..., N$ (first $N$ natural numbers) are there where the sum of every two adjacent numbers is at most $M$
1
vote
1answer
31 views
How many combinations for 3 cards from a deck of 52 cards if they have to be in ascending order?
If I wanted the different 3-card possible combinations from a total of 4 cards in ascending order, I would have:
$(1,2,3)$
$(1,2,4)$
$(1,3,4)$
$(2,3,4)$
How can I get all the possible triplets ...
3
votes
2answers
69 views
Prove or disprove ${{2a-1\choose a} + {2a-3\choose a-1} + {2a-5\choose a-2} + \dots {1\choose 1}}={2a\choose a+1}$
Prove or disprove $\displaystyle{{2a-1\choose a} + {2a-3\choose a-1} + {2a-5\choose a-2} + \dots {1\choose 1}}={2a\choose a+1}$
This is not homework. I'm trying to prove something related to Catalan ...
0
votes
0answers
19 views
beads in a string with restrictions
Using the principle of inclusion and exclusion; let $p,q\in \mathbb{N}$, being $p$ odd, there are $pq$ beads of $q$ differente colors, with $p$ beads in each color. if the beads of the same colour are ...
6
votes
0answers
71 views
looking for proof of determinant conjecture
Math people:
I am looking for a proof of a conjecture I made. I need a few definitions first. For distinct real numbers $x_1, x_2, \ldots, x_n$, define $\sigma(x_1, x_2, \ldots, x_n) =1$ if $(x_1, ...
0
votes
1answer
15 views
distinguishable and indistinguishable people and ticket offices
In how many ways we can arrange p people in the queue to the 5 ticet offices
a) people are distinguishable ticket offices are distinguishable
b) people are distinguishable ticket offices are ...
2
votes
2answers
48 views
Why placing people in a circle has (n-1)! distinct arrangements?
Why placing people in a circle has (n-1)! distinct arrangements?
I saw in books something about a placing a 'pivot',
But As i continued reading i saw something that really confused me. Once we can ...
1
vote
1answer
25 views
Permutation and Combination - Algebraic Expansion
I have come across the following question and solution
Question
In how many different ways three persons A, B, C having 6, 7 and 8 one rupee coins respectively can donate Rs.10 collectively.
...
2
votes
3answers
43 views
looking for a combinatorial interpretation
given positive integers $n,m$ does the fraction
$$
\frac{(nm)!}{n!^mm!}
$$
count something? Namely does it correspond to the number of possibilities to do something?
3
votes
1answer
26 views
Balls arrangements in a line
We randomly arrange balls numbered 1-100 in a line. What is the probability that there is a spot which splits the balls into two groups: All the balls preceding the splitting point are placed in ...
20
votes
3answers
738 views
A gambler with the devil's luck?
A gambler with $1$ dollar intends to make repeated bets of $1$ dollar until he wins $20$ dollars or is ruined. Probabilities of win/loss are $p$ and $(1-p)$, and each bet brings a gain/loss of $1$ ...
