Recent questions in Combinatory

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1

#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n-1}} + \sqrt{a_{n-2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (-1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n-1)^3$ $(n-1)^2$

asked Jun 5 in Combinatory by `JEET Active (3.3k points) | 57 views

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2

#Rosen exercise-1 ,question-71 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

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3

Self Doubt-Combinatory
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

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4

Rosen 7e Exercise-8.5 Question-15 page no-558 Inclusion-Exclusion
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 Active (3.7k points) | 62 views

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5

Recurrence Relation Self-Doubt
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 Active (3.7k points) | 36 views

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6

Rosen 7e Exercise 8.2 Questionno-26 page no-525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n-1}$-$12a_{n-2}$+$8a_{n-3}$+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 Active (3.7k points) | 32 views

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7

Rosen 7e Exercise-8.2 Question no-23 page no-525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n-1}$+$2^n$ 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 Active (3.7k points) | 22 views

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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 Active (1.1k points) | 34 views

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9

ISI2018-MMA-26
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 Boss (40.4k points) | 105 views

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10

ISI2018-MMA-10
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

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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

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12

ISI2019-MMA-27
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

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13

ISI2019-MMA-20
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

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1 answer

14

ISI2019-MMA-4
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

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15

ISI2019-MMA-2
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 points) | 230 views

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16

Rosen 7e Recurrence Relation Exercise-8.1 Question no-25 page no-511
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 n-1 having odd number of 0s T(n)=T(n-1) Hence, we have T(n)=2T(n-1)

asked Apr 29 in Combinatory by aditi19 Active (3.7k points) | 39 views

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17

Rosen 7e Exercise-8.1 Question no-10 Page no-511
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

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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

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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

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1 answer

20

Rosen 7e Exercise-6.5 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

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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

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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

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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

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24

General Query: Self doubt(Math+Automata)
Can somebody explain What is identity permutation?

asked Apr 1 in Combinatory by srestha Veteran (111k points) | 23 views

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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

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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

+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

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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 $a)3\left ( 1+3x \right )^{-2}$ $b)3\left ( 1-3x \right )^{-2}$ $c)2\left ( 1+3x \right )^{-3}$ $d)2\left ( 1-3x \right )^{-3}$

asked Mar 8 in Combinatory by srestha Veteran (111k points) | 62 views

+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

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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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