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Recent questions tagged combinatory

0 votes
1 answer
751
NPTEL Question
Find the particular solution of the given Recurrence relation or Difference equation. ar - 5ar-1 + 6ar-2 = 2r + r
Find the particular solution of the given Recurrence relation or Difference equation.ar - 5ar-1 + 6ar-2 = 2r + r
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0 votes
0 answers
753
#first course in probability #sheldon_ross 8th edition Qn. #10(c)
In how many ways can 8 people be seated in a row if there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?
In how many ways can 8 people be seated in a row if there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?
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0 votes
1 answer
755
#combinotirics
Find the largest integer value of x such that the following inequality holds: (10 C x-1) <2*(10 C x) In this question if solved line by line i am getting x<6. but clearly if you put x=7, it satisfies the inequality and 7 becomes the largest integer. Is there a procedure to get answer 7 step by step??
Find the largest integer value of x such that the following inequality holds:(10 C x-1) <2*(10 C x)In this question if solved line by line i am getting x<6.but clearly if...
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1 votes
2 answers
756
Kenneth Rosen Edition7th Exercise 6.1 Example 20 (Page No. 394)
what does it mean that "each person has same left and right neighbour "?
what does it mean that "each person has same left and right neighbour "?
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3 votes
1 answer
758
Seldon Ross
How many 5 digit numbers can be formed from the integers 1,2......9 if no digit can appear more than twice?
How many 5 digit numbers can be formed from the integers 1,2......9 if no digit can appear more than twice?
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1 votes
0 answers
759
Is Summation topic in GATE syllabus
Is summation is in Gate 2018 syllabus?
Is summation is in Gate 2018 syllabus?
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4 votes
2 answers
760
Combination (Repetition)
A girl has to choose 4 items from a bucket which contains 3 red, 3 green, and 4 blue balls, now in how many ways she can do this?
A girl has to choose 4 items from a bucket which contains 3 red, 3 green, and 4 blue balls, now in how many ways she can do this?
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2 votes
3 answers
762
Permutations
How many different words of 3 length can be formed from a,e,i,o,u containing a,e ?
How many different words of 3 length can be formed from a,e,i,o,u containing a,e ?
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2 votes
1 answer
764
How to find this coefficient in this question?
Find coeff of x^83 in [x^83].(x^5+x^8+x^11+x^14+x^17)
Find coeff of x^83 in [x^83].(x^5+x^8+x^11+x^14+x^17)
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1 votes
1 answer
765
What's the coefficient of this expansion??
What's the coefficient of $x^7$ in $(2x+4)^{10}$?
What's the coefficient of $x^7$ in $(2x+4)^{10}$?
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1 votes
2 answers
768
How to solve this generating function Question
Given two each of p kinds of objects and one each of additional q kind of objects, in how many ways r objects can be selected? Please give a detailed solution.
Given two each of p kinds of objects and one each of additional q kind of objects, in how many ways r objects can be selected?Please give a detailed solution.
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4 votes
1 answer
770
gatebook
How many bit strings of length $6$ have more no of zeros than ones?? We can solve this drawing tree but it takes so much time Is there any other way??
How many bit strings of length $6$ have more no of zeros than ones??We can solve this drawing tree but it takes so much time Is there any other way??
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1 votes
1 answer
772
kenneth rosen chapter 8 section 8.4 example 10
The coefficient of $x^{17}$ in the expansion of $(x^2 + x^3 + x^4 + x^5)*(x^3 + x^4 + x^5 + x^6)*(x^4 + x^5 + x^6 + x^7).$
The coefficient of $x^{17}$ in the expansion of $(x^2 + x^3 + x^4 + x^5)*(x^3 + x^4 + x^5 + x^6)*(x^4 + x^5 + x^6 + x^7).$
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5 votes
1 answer
773
Discrete Mathematics for Computer Scientists and Mathematicians , Chapter- 2 , Exercise- 2.2, Question-4
1- Determine the number of 5-combinations of { 1.a , ∞.b ,∞.c , 1.d }. 2-More generally , develop a formula for the number of r-combinations of a collection of letter...
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2 votes
0 answers
774
Discrete Mathematics for Computer Scientists and Mathematicians , Chapter- 2 , Exercise- 2.1, Question-36
Twenty athletes compete in a contest. Each of 3 judges assign 20 different ratings to the 20 athletes. For an athlete to be named winner he must be given the highest rati...
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1 votes
0 answers
777
Integer Sequence
... $\begin{align*} |A| = |B| \end{align*}$
$\begin{align*} &\text{A} = \text{Set of integer sequence }\left ( a_1,a_2,a_2 ,\dots , a_k \right ) \\ &\text{where } 1 \leq a_1 \leq a_2 \leq a_3 \leq \dots \leq a_k \l...
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1 votes
0 answers
778
Combinatoric properties
Prove that : $\begin{align*} &\text{For n , k , m are integers and } 0 < m \leq k < n \\ &\text{GCD}\left [ \binom{n}{m},\binom{n}{k} \right ] > 1 \\ \end{align*}$
Prove that :$\begin{align*} &\text{For n , k , m are integers and } 0 < m \leq k < n \\ &\text{GCD}\left [ \binom{n}{m},\binom{n}{k} \right ] 1 \\ \end{align*}$
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4 votes
1 answer
779
Combinatory
How many ordered quadruples $\left ( x_{1},x_{2},x_{3},x_{4} \right )$ of odd positive integers satisfy $x_{1}+x_{2}+x_{3}+x_{4}=98?$
How many ordered quadruples $\left ( x_{1},x_{2},x_{3},x_{4} \right )$ of odd positive integers satisfy$$x_{1}+x_{2}+x_{3}+x_{4}=98?$$
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