Recent questions and answers in Combinatory

+18 votes

5 answers

1

GATE2000-1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$

answered 21 hours ago in Combinatory by Asim Siddiqui 4 Active (1.2k points) | 2.9k views

+38 votes

6 answers

2

GATE2005-44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$

answered 3 days ago in Combinatory by techbd123 Active (1.4k points) | 4.2k views

+3 votes

2 answers

3

CMI2015-A-10
The school athletics coach has to choose 4 students for the relay team. He calculates that there are 3876 ways of choosing the team if the order in which the runners are placed is not considered. How many ways are there of choosing the team if the order of the ... taken into account? Between 12,000 and 25,000 Between 75,000 and 99,999 Between 30,000 and 60,000 More than 100,000

answered 3 days ago in Combinatory by chirudeepnamini Active (1.8k points) | 92 views

0 votes

1 answer

4

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)

answered 6 days ago in Combinatory by anonymousgamer (11 points) | 53 views

0 votes

1 answer

5

Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?

answered Oct 11 in Combinatory by shivamgo (11 points) | 29 views

+5 votes

10 answers

6

GATE2019-21
The value of $3^{51} \text{ mod } 5$ is _____

answered Oct 3 in Combinatory by techbd123 Active (1.4k points) | 3k views

0 votes

3 answers

7

Permutations and combinations
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?

answered Sep 13 in Combinatory by gajendercse (11 points) | 252 views

+5 votes

2 answers

8

permutation combo
In how many ways can seven different jobs be assigned to 4 different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee?

answered Sep 3 in Combinatory by aditi19 Active (4.9k points) | 374 views

+2 votes

2 answers

9

Combinatoric
Find number of zero's at the end of (2018)! ?

answered Sep 3 in Combinatory by Lakshman Patel RJIT Veteran (51.5k points) | 60 views

+1 vote

2 answers

10

Pigeon hole
Show that in a group of $n$ people there are two who have identical number of friends in that group.

answered Aug 24 in Combinatory by chirudeepnamini Active (1.8k points) | 48 views

+15 votes

5 answers

11

TIFR2013-A-9
There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^{n} . n!}$ $\frac{n!}{2}$ None of the above.

answered Aug 22 in Combinatory by Verma Ashish Boss (10.7k points) | 826 views

+20 votes

4 answers

12

GATE2000-5
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be constructed from n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?

answered Aug 21 in Combinatory by Verma Ashish Boss (10.7k points) | 1.5k views

+5 votes

7 answers

13

TIFR2018-B-1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$

answered Aug 21 in Combinatory by Verma Ashish Boss (10.7k points) | 399 views

+3 votes

1 answer

14

ISI MTECH CS 2019 INTERVIEW question
As due to rain, the match between the teams in ICC world cup got canceled , So lets the total team be 10, exclude semi finals and finals , consider only league match, What is the total number of matches that played between the teams ... many ways those n matches can be conducted ? Source : https://gateoverflow.in/blog/8548/isi-mtech-cs-2019-interview-experience

answered Aug 8 in Combinatory by Shaik Masthan Veteran (63.6k points) | 121 views

+1 vote

2 answers

15

UGCNET-June-2019-II-3
How many bit strings of length ten either start with a $1$ bit or end with two bits $00$ ? $320$ $480$ $640$ $768$

answered Jul 23 in Combinatory by Lakshman Patel RJIT Veteran (51.5k points) | 207 views

+14 votes

4 answers

16

GATE2007-IT-76
Consider the sequence $\langle x_n \rangle , \: n \geq 0$ defined by the recurrence relation $x_{n+1} = c . x^2_n -2$, where $c > 0$. Suppose there exists a non-empty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges ... sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1-\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c-1}$

answered Jul 20 in Combinatory by ankitgupta.1729 Boss (15.4k points) | 1.3k views

+8 votes

8 answers

17

Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

answered Jul 14 in Combinatory by srestha Veteran (116k points) | 2.3k views

+1 vote

2 answers

18

UGCNET-June-2019-II-2
How many ways are there to place $8$ indistinguishable balls into four distinguishable bins? $70$ $165$ $^8C_4$ $^8P_4$

answered Jul 13 in Combinatory by Lakshman Patel RJIT Veteran (51.5k points) | 289 views

+2 votes

2 answers

19

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?

answered Jul 11 in Combinatory by srestha Veteran (116k points) | 254 views

+9 votes

4 answers

20

ISI 2004 MIII
The number of permutation of $\{1,2,3,4,5\}$ that keep at least one integer fixed is. $81$ $76$ $120$ $60$

answered Jul 9 in Combinatory by Debargha Bhattacharj Junior (653 points) | 660 views

+10 votes

6 answers

21

TIFR2015-A-7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$

answered Jul 7 in Combinatory by Bishal1997 (11 points) | 744 views

+2 votes

1 answer

22

UGCNET-June-2019-II-63
Consider the Euler’s phi function given by $\phi(n) = n \underset{p/n}{\Pi } \bigg( 1 – \frac{1}{p} \bigg)$ where $p$ runs over all the primes dividing $n$. What is the value of $\phi(45)$? $3$ $12$ $6$ $24$

answered Jul 6 in Combinatory by Ram Swaroop Active (4.2k points) | 80 views

+1 vote

3 answers

23

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 Jul 6 in Combinatory by venkatesh pagadala Junior (555 points) | 303 views

0 votes

1 answer

24

Four cups and saucers
A tea set has four cups and saucers with two cups and saucers in each of two different colours. If the cups are placed at random on the saucers, what is the probability that no cup is on a saucer of the same colour?

answered Jul 4 in Combinatory by Yash4444 Junior (609 points) | 36 views

0 votes

2 answers

25

Permutation and combination
9 different books are to be arranged on a bookshelf. 4 of these books were written by Shakespeare, 2 by Dickens, and 3 by Conrad. How many possible permutations are there if the books by Conrad must be separated from one another?

answered Jul 3 in Combinatory by Gurdeep Saini Boss (10.1k points) | 124 views

+1 vote

1 answer

26

UGCNET-June-2019-II-7
How many cards must be selected from a standard deck of $52$ cards to guarantee that at least three hearts are present among them? $9$ $13$ $17$ $42$

answered Jul 2 in Combinatory by Satbir Boss (19.5k points) | 154 views

0 votes

3 answers

27

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 Jul 2 in Combinatory by sahil bhalla (11 points) | 96 views

+6 votes

6 answers

28

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 26 in Combinatory by Arkaprava Active (2.2k points) | 429 views

+14 votes

6 answers

29

GATE2005-50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$

answered Jun 25 in Combinatory by Satbir Boss (19.5k points) | 1.5k views

0 votes

1 answer

30

Kenneth Rosen: Counting-13
How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$

answered Jun 25 in Combinatory by srestha Veteran (116k points) | 89 views

+23 votes

12 answers

31

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

answered Jun 19 in Combinatory by Kuldeep Pal Active (1.4k points) | 8k views

+41 votes

11 answers

32

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 Jun 19 in Combinatory by Kuldeep Pal Active (1.4k points) | 4.1k views

+25 votes

7 answers

33

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 Jun 19 in Combinatory by Kuldeep Pal Active (1.4k points) | 2.8k views

+19 votes

3 answers

34

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 (1.4k points) | 888 views

+35 votes

7 answers

35

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 Junior (967 points) | 5.6k views

+15 votes

8 answers

36

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 (1.4k points) | 6k views

+20 votes

3 answers

37

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 (51 points) | 3.9k views

0 votes

0 answers

38

#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 Loyal (8.2k points) | 108 views

0 votes

0 answers

39

#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 (259 points) | 36 views

0 votes

2 answers

40

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 (4.9k points) | 79 views

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

Recent questions and answers in Combinatory

Recent Posts

Recent Blog Comments