I have three kinds of items (infinite supply): $a$, $b$ and $c$. I want to choose freely from the infinite large collection of items and put them in $n$ number of boxes. However: Only one item is allowed in each box and I am not allowed to put item a in the first box. Neither am I allowed to let neither $a$:s nor $c$:s be in adjacent boxes. What are all the possible combinations I can get and how many permutations are there for each combination if there are $n$ number of boxes?
2026-03-25 07:46:04.1774424764
All combinations and number of permutions of each combination with three kinds of items
85 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMBINATORICS
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Hard combinatorial identity: $\sum_{l=0}^p(-1)^l\binom{2l}{l}\binom{k}{p-l}\binom{2k+2l-2p}{k+l-p}^{-1}=4^p\binom{k-1}{p}\binom{2k}{k}^{-1}$
- Algebraic step including finite sum and binomial coefficient
- nth letter of lexicographically ordered substrings
- Count of possible money splits
- Covering vector space over finite field by subspaces
- A certain partition of 28
- Counting argument proof or inductive proof of $F_1 {n \choose1}+...+F_n {n \choose n} = F_{2n}$ where $F_i$ are Fibonacci
Related Questions in PERMUTATIONS
- A weird automorphism
- List Conjugacy Classes in GAP?
- Permutation does not change if we multiply by left by another group element?
- Validating a solution to a combinatorics problem
- Selection of at least one vowel and one consonant
- How to get the missing brick of the proof $A \circ P_\sigma = P_\sigma \circ A$ using permutations?
- Probability of a candidate being selected for a job.
- $S_3$ action on the splitting field of $\mathbb{Q}[x]/(x^3 - x - 1)$
- Expected "overlap" between permutations of a multiset
- Selecting balls from infinite sample with certain conditions
Related Questions in COMBINATIONS
- Selection of "e" from "e"
- Selection of at least one vowel and one consonant
- Probability of a candidate being selected for a job.
- Proving that no two teams in a tournament win same number of games
- Selecting balls from infinite sample with certain conditions
- Divide objects in groups so that total sum of sizes in a group are balanced across groups
- Value of n from combinatorial equation
- Number of binary sequences with no consecutive ones.
- Count probability of getting rectangle
- Sum of all numbers formed by digits 1,2,3,4 & 5.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Well... I made a series of matrices and tried to figure out the patterns. Since b is allowed to be placed anywhere, let us let the exponent of b be equal to the total number of variables minus the sum of exponents of the other two variables. I found, that if one of the variables a and c are non-present the coeffcient can be derived from Pascal's triangel. All 1:s have coefficents 1,2,3,4,5... all 2:s 1,3,6,10,15 ... all 3:s 1,4,10,20... etc. If a and c are 1, then the coeffeficient is a perfect square. If there are 2 c:s and 1 a they seem to be 1*2, 3*3, 6*4, 10*5... and 1*3, 3*4, 6*5, 10*6 ... for 3 a:s. If there are 2 c:s and 1 a they are 1 , 5, 15 ... As for a^2c^2, I beleive they are 1, 7, 28 ...
So ... There are clearly patterns here, but it is hard to work it out without running a simulation. This is actually part of a larger probability problem I am working with. I really should learn programming! The online calculators are very good, but you can't make algorithms for solvning problems and making many simultanious calculations. Online calculators also collaps when the expressions you put in get too massive.