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Combinatorics:
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Recurrence relations,
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#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n1}} + \sqrt{a_{n2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
asked
Jun 5
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Combinatory
by
`JEET
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3.3k
points)

57
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discretemathematics
permutationsandcombinations
recurrence
#recurrencerelations
0
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0
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2
#Rosen exercise1 ,question71 counting
use mathematical induction to prove the sum rule for m tasks from the sum rule for two tasks.
asked
May 31
in
Combinatory
by
sandeep singh gaur
(
243
points)

21
views
counting
0
votes
2
answers
3
Self DoubtCombinatory
In how many ways we can put $n$ distinct balls in $k$ dintinct bins?? Will it be $n^{k}$ or $k^{n}$?? Taking example will be easy way to remove this doubt or some other ways possible??
asked
May 25
in
Combinatory
by
srestha
Veteran
(
111k
points)

58
views
discretemathematics
permutationsandcombinations
0
votes
2
answers
4
Rosen 7e Exercise8.5 Question15 page no558 InclusionExclusion
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?
asked
May 24
in
Combinatory
by
aditi19
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3.7k
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62
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discretemathematics
kennethrosen
inclusionexclusion
0
votes
1
answer
5
Recurrence Relation SelfDoubt
What will be solution of recurrence relation if roots are like this: r1=2, r2=2, r3=2, r4=2 is this the case of repetitive roots?
asked
May 14
in
Combinatory
by
aditi19
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3.7k
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36
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relations
recurrence
recurrenceeqation
discretemathematics
combinational
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6
Rosen 7e Exercise 8.2 Questionno26 page no525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n1}$$12a_{n2}$+$8a_{n3}$+F(n) if F(n)=$n^2$ F(n)=$2^n$ F(n)=$n2^n$ F(n)=$(2)^n$ F(n)=$n^22^n$ F(n)=$n^3(2)^n$ F(n)=3
asked
May 14
in
Combinatory
by
aditi19
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3.7k
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32
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kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
0
answers
7
Rosen 7e Exercise8.2 Question no23 page no525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n1}$+$2^n$ in the book solution is given $a_n$=$2^{n+1}$ but I’m getting $a_n$=$3^{n+1}2^{n+1}$
asked
May 13
in
Combinatory
by
aditi19
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3.7k
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22
views
kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
2
answers
8
#probability(self doubt)
An automobile showroom has 10 cars, 2 of which are defective. If you are going to buy the 6th car sold that day at random, then the probability of selecting a defective car is??
asked
May 13
in
Combinatory
by
G Shaheena
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1.1k
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34
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#probability
self
doubt
+1
vote
1
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9
ISI2018MMA26
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}\dots +(1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
asked
May 11
in
Combinatory
by
akash.dinkar12
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(
40.4k
points)

105
views
isi2018
engineeringmathematics
discretemathematics
generatingfunctions
0
votes
1
answer
10
ISI2018MMA10
A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done so that no two adjacent strips have the same color? $120$ $324$ $424$ $576$
asked
May 11
in
Combinatory
by
akash.dinkar12
Boss
(
40.4k
points)

28
views
isi2018
engineeringmathematics
discretemathematics
permutationsandcombinations
0
votes
1
answer
11
A first course in probability by Sheldon Ross
What are the relevant chapter of probability by sheldon ross to study for gate? I think whole syllabus is within chapter 5,Should i study everything upto chapter 5 or there are some topics that can be skipped.
asked
May 8
in
Combinatory
by
souren
(
37
points)

44
views
probability
sheldonross
0
votes
2
answers
12
ISI2019MMA27
A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold the election? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
asked
May 7
in
Combinatory
by
Sayan Bose
Loyal
(
6.9k
points)

2.8k
views
isi2019
engineeringmathematics
discretemathematics
permutationsandcombinations
0
votes
2
answers
13
ISI2019MMA20
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter ‘O’ and the digit ‘0’ are not used in the same number plate. How many such number plates can be formed? $164025$ $190951$ $194976$ $219049$
asked
May 7
in
Combinatory
by
Sayan Bose
Loyal
(
6.9k
points)

317
views
isi2019
engineeringmathematics
discretemathematics
permutationsandcombinations
0
votes
1
answer
14
ISI2019MMA4
Suppose that $6$digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$digit numbers that are divisible by $6$ but not divisible by $9$ is equal to $120$ $180$ $240$ $360$
asked
May 6
in
Combinatory
by
Sayan Bose
Loyal
(
6.9k
points)

192
views
isi2019
engineeringmathematics
discretemathematics
permutationsandcombinations
0
votes
1
answer
15
ISI2019MMA2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$
asked
May 6
in
Combinatory
by
Sayan Bose
Loyal
(
6.9k
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230
views
isi2019
engineeringmathematics
discretemathematics
permutationsandcombinations
0
votes
0
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16
Rosen 7e Recurrence Relation Exercise8.1 Question no25 page no511
How many bit sequences of length seven contain an even number of 0s? I'm trying to solve this using recurrence relation Is my approach correct? Let T(n) be the string having even number of 0s T(1)=1 {1} T(2)=2 {00, 11} T(3)=4 {001, ... add 0 to strings of length n1 having odd number of 0s T(n)=T(n1) Hence, we have T(n)=2T(n1)
asked
Apr 29
in
Combinatory
by
aditi19
Active
(
3.7k
points)

39
views
kennethrosen
discretemathematics
permutationsandcombinations
#recurrencerelations
recurrence
0
votes
1
answer
17
Rosen 7e Exercise8.1 Question no10 Page no511
Find a recurrence relation for the number of bit strings of length n that contain the string 01.
asked
Apr 28
in
Combinatory
by
aditi19
Active
(
3.7k
points)

38
views
kennethrosen
discretemathematics
permutationsandcombinations
#recurrencerelations
recurrence
+1
vote
1
answer
18
Pgee 2013
You have a box containing 10 black and 10 blue socks.What is the minimum number of times you need to pull out so that you have a pair of the same color?
asked
Apr 22
in
Combinatory
by
Winner
(
249
points)

87
views
iiithpgee
0
votes
0
answers
19
Kenneth H Rosen 7th edition
Please see example 6. l am not getting the mathematical insight. Can anyone please tell how they are arriving at the answer.
asked
Apr 21
in
Combinatory
by
Psnjit
(
191
points)

43
views
kennethrosen
discretemathematics
permutationsandcombinations
+2
votes
1
answer
20
Rosen 7e Exercise6.5 question 45.b page 433
How many ways can n books be placed on k distinguishable shelves if no two books are the same, and the positions of the books on the shelves matter?
asked
Apr 16
in
Combinatory
by
aditi19
Active
(
3.7k
points)

158
views
kennethrosen
discretemathematics
permutationsandcombinations
0
votes
1
answer
21
Madeeasy Discrete Maths notes
How many 5 letter word possible having atleast 2 a's ?
asked
Apr 9
in
Combinatory
by
Prakhar Garg
(
61
points)

62
views
madeeasynotes
discretemathematics
permutationsandcombinations
0
votes
1
answer
22
Self doubt
How is the problem.. Distribute 5 toys such that each of 3 child get atleast 1 Different from sum of 3 no. X+y+z=5 such that each digit >= 1. Plz explain ?
asked
Apr 4
in
Combinatory
by
Manoj Kumar Pandey
(
141
points)

56
views
permutationsandcombinations
0
votes
0
answers
23
Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?
asked
Apr 2
in
Combinatory
by
Manoj Kumar Pandey
(
141
points)

18
views
permutationsandcombinations
0
votes
0
answers
24
General Query: Self doubt(Math+Automata)
Can somebody explain What is identity permutation?
asked
Apr 1
in
Combinatory
by
srestha
Veteran
(
111k
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23
views
discretemathematics
finiteautomata
0
votes
0
answers
25
website
There is 4 coins 1 paisa, 5 paise, 10 paise, 25 paise using these coins we have to make 50 paisa how many combination can we make ?
asked
Mar 31
in
Combinatory
by
Cristine
Active
(
1.7k
points)

26
views
permutationsandcombinations
0
votes
0
answers
26
Allen Career Institute: Discrete Mathematics
A certain software was being tested by using error seeding strategy in which $22$ errors were seeded. $14$ of seeded errors were detected apart from $140$ unseeded errors when the code was tested using the complete test suit. Calculate the estimated no. of undetected errors in the code after complete testing _____
asked
Mar 22
in
Combinatory
by
srestha
Veteran
(
111k
points)

29
views
discretemathematics
permutationsandcombinations
+1
vote
1
answer
27
Model Question IISc CDS CS Written Test Sample question
Anand is preparing a pizza with 8 slices, and he has 10 toppings to put on the pizza. He can put only one topping on each slice but can use the same topping on zero or more slices. In how many unique ways can he prepare the slices so that the same topping is not used in adjacent slices?
asked
Mar 11
in
Combinatory
by
Chaitrasj
Junior
(
925
points)

192
views
iisc
cds
0
votes
1
answer
28
ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{2}$ $b)3\left ( 13x \right )^{2}$ $c)2\left ( 1+3x \right )^{3}$ $d)2\left ( 13x \right )^{3}$
asked
Mar 8
in
Combinatory
by
srestha
Veteran
(
111k
points)

62
views
generatingfunctions
discretemathematics
+2
votes
1
answer
29
Rosen 7e, Advance Counting techniques , Question 6.f
Find the generating function for the sequence $\left \{ a_n \right \} where $ $a_n = \Large \binom{10}{n+1} $ ... $\Large \color{red}{ \frac{( 1+x )^{10}  1}{x} }$ Please verify
asked
Mar 7
in
Combinatory
by
Mk Utkarsh
Boss
(
34.5k
points)

42
views
kennethrosen
discretemathematics
generatingfunctions
0
votes
1
answer
30
Rosen Ex.6.1
Find a recurrence relation for the number of ways to lay out a walkway with slate tiles if the tiles are red, green, or gray so that no two red tiles are adjacent and tiles of the same color are considered indistinguishable
asked
Mar 3
in
Combinatory
by
himgta
Active
(
3.5k
points)

32
views
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