Recent questions and answers in Combinatory

+20 votes

12 answers

1

GATE2018-46
The number of possible min-heaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______

answered 5 days ago in Combinatory by Kuldeep Pal Active (1.3k points) | 7.3k views

+37 votes

11 answers

2

GATE2015-3-5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.

answered 5 days ago in Combinatory by Kuldeep Pal Active (1.3k points) | 3.8k views

+23 votes

7 answers

3

GATE2004-IT-35
In how many ways can we distribute $5$ distinct balls, $B_1, B_2, \ldots, B_5$ in $5$ distinct cells, $C_1, C_2, \ldots, C_5$ such that Ball $B_i$ is not in cell $C_i$, $\forall i= 1,2,\ldots 5$ and each cell contains exactly one ball? $44$ $96$ $120$ $3125$

answered 5 days ago in Combinatory by Kuldeep Pal Active (1.3k points) | 2.5k views

+1 vote

2 answers

4

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?

answered 5 days ago in Combinatory by Satbir Boss (13.2k points) | 205 views

+19 votes

3 answers

5

TIFR2014-A-5
The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students? $23$ $91$ $60$ $49$ None of the above.

answered Jun 17 in Combinatory by Kuldeep Pal Active (1.3k points) | 821 views

+34 votes

7 answers

6

GATE2017-2-47
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .

answered Jun 17 in Combinatory by mohan123 (135 points) | 5.4k views

+13 votes

8 answers

7

GATE2018-1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$

answered Jun 17 in Combinatory by Kuldeep Pal Active (1.3k points) | 5.7k views

+17 votes

3 answers

8

GATE1999-2.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above

answered Jun 14 in Combinatory by bruce-bayne (21 points) | 3.6k views

0 votes

2 answers

9

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??

answered Jun 9 in Combinatory by Koushik Sinha 2 (253 points) | 61 views

+3 votes

5 answers

10

TIFR2019-B-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 red or a blue house must be green. How many ways are there to paint the houses? $199$ $683$ $1365$ $3^{10}-2^{10}$ $3^{10}$

answered Jun 8 in Combinatory by shaktisingh (91 points) | 280 views

0 votes

1 answer

11

ISI2017-MMA-26
Let $n$ be the number of ways in which 5 men and 7 women can stand in a queue such that all the women stand consecutively. Let $m$ be the number of ways in which the same 12 persons can stand in a queue such that exactly 6 women stand consecutively. Then the value of $\frac{m}{n}$ is $5$ $7$ $5/7$ $7/5$

answered Jun 7 in Combinatory by venkatesh pagadala (495 points) | 27 views

0 votes

0 answers

12

#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) | 67 views

0 votes

0 answers

13

#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) | 22 views

0 votes

1 answer

14

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.

answered May 27 in Combinatory by Asim Siddiqui 4 Junior (843 points) | 46 views

0 votes

2 answers

15

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?

answered May 26 in Combinatory by aditi19 Active (3.7k points) | 64 views

0 votes

2 answers

16

UGCNET-Dec2012-III-25
The number of distinct bracelets of five beads made up of red, blue and green beads (two bracelets are indistinguishable if the rotation of one yield another) is, 243 81 51 47

answered May 15 in Combinatory by Kuljeet Shan Active (1.5k points) | 1.6k views

0 votes

1 answer

17

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?

answered May 14 in Combinatory by Raghava45 (331 points) | 37 views

0 votes

2 answers

18

Recurrence Relation
Let $T(n) = T(n-1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $ $O(n^{2})$ $O(logn)$ $O(nlogn)$ $O(n^{2}logn)$

answered May 14 in Combinatory by Raghava45 (331 points) | 135 views

0 votes

0 answers

19

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) | 34 views

0 votes

0 answers

20

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) | 23 views

0 votes

1 answer

21

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? $120$ $324$ $424$ $576$

answered May 13 in Combinatory by Sayan Bose Loyal (6.9k points) | 31 views

0 votes

2 answers

22

#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??

answered May 13 in Combinatory by srestha Veteran (111k points) | 34 views

+1 vote

1 answer

23

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 $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$

answered May 11 in Combinatory by srestha Veteran (111k points) | 107 views

0 votes

2 answers

24

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? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$

answered May 11 in Combinatory by amolcharpe (27 points) | 2.8k views

0 votes

2 answers

25

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? $164025$ $190951$ $194976$ $219049$

answered May 9 in Combinatory by Utkarsh Joshi Loyal (7.6k points) | 320 views

0 votes

1 answer

26

ISI2019-MMA-2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$

answered May 6 in Combinatory by pratekag Active (2k points) | 231 views

0 votes

1 answer

27

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 $120$ $180$ $240$ $360$

answered May 6 in Combinatory by pratekag Active (2k points) | 193 views

0 votes

1 answer

28

UPPCL AE 2018:66

answered May 3 in Combinatory by Abhisek Tiwari 4 Active (4.5k points) | 26 views

0 votes

2 answers

29

Suppose a 6 digit number N is formed by rearranging the digits of the number 123456

answered May 1 in Combinatory by kratos (11 points) | 535 views

0 votes

0 answers

30

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) | 40 views

0 votes

1 answer

31

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.

answered Apr 28 in Combinatory by srestha Veteran (111k points) | 38 views

+1 vote

1 answer

32

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?

answered Apr 22 in Combinatory by Manas Mishra Active (2.8k points) | 89 views

0 votes

0 answers

33

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) | 45 views

+2 votes

1 answer

34

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?

answered Apr 20 in Combinatory by ma1999 (11 points) | 170 views

0 votes

1 answer

35

Madeeasy Discrete Maths notes
How many 5 letter word possible having atleast 2 a's ?

answered Apr 9 in Combinatory by tusharp Loyal (6.5k points) | 65 views

0 votes

1 answer

36

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 ?

answered Apr 4 in Combinatory by hitendra singh Active (1.7k points) | 57 views

0 votes

0 answers

37

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

0 votes

0 answers

38

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

0 votes

0 answers

39

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 (1.8k points) | 26 views

+1 vote

3 answers

40

MadeEasy Subject Test 2019: Combinatory - Permutations And Combinations
Q.The number of ways, we can arrange 5 books in 3 shelves ________.

answered Mar 26 in Combinatory by Arkaprava Active (1.8k points) | 369 views

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