Combinatorics problems
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Q1. A plane has 15 points, 5 of them are collinear. Other than this, if no 3 points are collinear, find the total number of triangles and straight lines that can be formed.
Q2. A country has N cities and N roads. Between any two cities, there is maximum one road. Prove that there is at least one city, starting from which you can come back to it again without travelling the same road twice.
Q3. A= {1, 2, 3…….20}. How many subsets of A, containing three elements, can be formed so that the sum of the elements is divisible by 3?
Q2. A country has N cities and N roads. Between any two cities, there is maximum one road. Prove that there is at least one city, starting from which you can come back to it again without travelling the same road twice.
Q3. A= {1, 2, 3…….20}. How many subsets of A, containing three elements, can be formed so that the sum of the elements is divisible by 3?
Re: Combinatorics problems
Have you solved this? If not,here are some hints
Hint:
$\text {Problem 1}$:
$\text {Problem 2}$:
$\text {Problem 3}$:
Hint:
$\text {Problem 1}$:
$\text {Problem 3}$:
"Questions we can't answer are far better than answers we can't question"
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Re: Combinatorics problems
I have solved them but I am uncertain about the solutions. Can you post the solutions?
Re: Combinatorics problems
Okay.Ragib Farhat Hasan wrote:I have solved them but I am uncertain about the solutions. Can you post the solutions?
$\text {Problem 1}$:
There is a cycle.So,it is possible.
$\text {Problem 3}$:
Last edited by tanmoy on Wed Sep 30, 2015 2:34 pm, edited 1 time in total.
"Questions we can't answer are far better than answers we can't question"
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- Posts:62
- Joined:Sun Mar 30, 2014 10:40 pm
Re: Combinatorics problems
Problem 3:
My answer is 6C3+(6)(7)(7)+7C3+7C3=384.
My answer is 6C3+(6)(7)(7)+7C3+7C3=384.
Re: Combinatorics problems
There was a typo.So,edited.Ragib Farhat Hasan wrote:Problem 3:
My answer is 6C3+(6)(7)(7)+7C3+7C3=384.
"Questions we can't answer are far better than answers we can't question"
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Re: Combinatorics problems
A card is selected at random from a standard 52 card deck. The suit is recorded and the card is replaced in the deck. This is done a total of seven times. find the probability of all four suits occur among the cards selected.
Re: Combinatorics problems
I think the probability is 3/32.
Total number of incidents is $4^7$.
There are $4!$x$4^3$ incidents where all four suits occure.
Total number of incidents is $4^7$.
There are $4!$x$4^3$ incidents where all four suits occure.