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Recent questions tagged counting

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indistinguishable objects distinguishable boxes
how to know when to apply which case for : in-distinguishable object in-distinguishable boxes.Example- 12 balls are distributed at random among three boxes.The probabilit...
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Counting
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MadeEasy Full Length Test 2018: Graph Theory - Counting
The Number of Labelled possible graph given below ? what I did was →we doesn’t remove any of the edge out of 4 = $\binom{4}{0}$ [Because a Graph is sub-graph of itse...
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UGC NET CSE | December 2018 | Part 2 | Question: 33
The number of substrings that can be formed from string given by$a \: d \: e \: f \: b \: g \: h \: n \: m \: p$is$10$$45$$55$$56$
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GATE Overflow | Mock GATE | Test 1 | Question: 54
Let $S$ be a set of $n$ elements $\{1, 2, \dots n\}$ and $G$ a graph with $2^n$ vertices, where each vertex corresponds to a distinct subset of $S$. Two vertices are adja...
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TIFR CSE 2019 | Part B | Question: 13
A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a r...
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#Combinations
Number of ways of splitting 10 people into 2 teams of 6 and 4 people respectively. Answer- $^{10}c_{6}$Number of ways of splitting 10 people into 2 teams of 5 people each...
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Kenneth Rosen Edition 6th Exercise 6.1 Example 7 (Page No. 399)
this is an example taken from Rosen. but I’m unable to understand to understand the solution given therecan someone pls explain me in details
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To find the total no of substring, why we are not counting null substring 
To find the total no of substring why we are not counting null substring https://stackoverflow.com/questions/12418590/finding-substrings-of-a-string https://gateoverflow....
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Zeal Test Series 2019: Graph Theory - Counting
Is there any short trick to do it ?
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Number of sub-strings for a given sub string having repeated symbols
Lets for a a given string aabbbccddI need to find the number of substrings possible how to go about it? Does the n(n+1)/2 formula work here also?
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Test series
R is a relation define on set A = {1,2,3}. The R is symmetric, transitive and irreflexive. Then |R| =
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Rosen-Pigeonhole Principle
How many cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?what this question means?
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Counting
A number of ways we can arrange letters of the word " TESTBOOK " such that E always comes between O's is ___________
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690
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Combinations
In how many ways a team of 11 players be selected from 14 players when two of them can play as goalkeepers only?
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TANCET 2016 Discrete Mathematics
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General Doubt on Generating Functions
Given only a Generating Function in closed form can we find the sequence it represents? If so, how? Please explain with an example.If not, given a GF(closed form) in gen...
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Kenneth Rosen: Counting-13
How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$
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Kenneth Rosen- Counting-3.a,b
A multiple choice test contains $10$ questions There are $4$ possible answers for each question?$a)$How many ways can a student answer the questions on the test if the st...
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cormen 7th edition counting
How many ways are there for a horse race with three horses to finish if ties are possible?(Note: Two or three horses may tie)My answer is 9 but correct answer is 13.In th...
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Kenneth Rosen Edition 7 Exercise 6.1 Question 45 (Page No. 397)
How many ways are there to seat six people around a circular table where two seating are considered the same when everyone has the same two neighbors without regard to wh...
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Counting
1)In how many ways we can put n distinct balls in k identical bins?2)In how many ways we can put n distinct balls in k identical bins such that no bin is empty?
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PigeonHole Principal
A drawer contains a dozen of brown and dozen of black socks,all unmatched.A man takes socks out at random in the dark. How many socks must he take out to be sure that he ...
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1 1 vote
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Kenneth Rosen Edition 6th Exercise 6.4 Example 15 (Page No. 435 )
How to find the coefficient ( for eg $x^7$ ) in the generating function$(1+x+x^2+x^3+..)(1+x^2+x^4+x^6+..)(1+x^5+x^{10}+x^{15}+..)$ ?
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MADEEASY
Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?
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Testbook Test Series: Graph Theory - Counting
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Combinatorics Question on Bit Strings
How many bit strings of length 8 contain either three consecutive 0's or four consecutive 1's ?MY APPROACH :-Initially, for 3 consecutive 0's:000_ _ _ _ _ =>2^5 = 32 WAYS...
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Kenneth Rosen Edition 6th Exercise 5.6 Example 5 (Page No. 385)
I am not getting this condition. Can someone please explain that condition with that example.
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Kenneth Rosen Edition 6th Exercise 6.4 Question 6 e (Page No. 440)
nC2 for n=0,1,2,3...
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Combinatorics
Among the integers $1,2,3,....,200$ if $101$ integers are chosen,then show that there are two among the chosen,such that one is divisible by the other.
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