A 'combination' lock has three numbers, each in the range 1-50.
How many have the first and second numbers matching?
How many have exactly two of the numbers matching?
All I know is that this a permutation case.
I'm not sure how to find the answer.
2026-04-24 14:21:27.1777040487
Combinations of a Combination lock
238 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
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?
The way to start the first one : every such combination is of the form $AAB$ where $A,B$ are in the range $1-50$.How many choices for $A$? How many for $B$?(How do you find the answer once you know these values?) Note that it is okay if $A=B$, we only want to find those for which the first two positions match.
To do the second one, we proceed by complementation, instead counting those for which there are no matches, or all three match.
How many have all three matching ? These are of the form $AAA$, so how many possibilities for $A$?
Those with none matching have $ABC$ with $A\neq B , B \neq C , A \neq C$. How many choices for $A$? How many choices for $B$, given the value of $A$? How many choices for $C$, given the values of both $B$ and $A$? Now multiply all of them.
Finally add these two and subtract from the total number of possible permutations (how many is that? This is the easiest of the lot).