All Questions
43
questions
1
vote
1
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172
views
Number of binary numbers given constraints on consecutive elements
I've been trying to solve this question for quite a while, given to us by our discrete maths professor. I've been having a hard time in general with it, so I thought I tried looking it up online but ...
- 27
1
vote
1
answer
395
views
Choose unique numbers from different sets
Suppose that there are n, possibly equal, non-empty sets. The problem is concerning choosing unique n numbers such that first ...
- 147
2
votes
0
answers
82
views
Revealed preference rank rule: variation on horse race problem
Suppose there are x number of objects to be ranked. Then there are x[(x-1)/2] possible comparisons of these objects. Only subsets of x can be evaluated for comparisons and there is always one most and ...
- 147
0
votes
0
answers
87
views
Minimum movements to arrange fruits in boxes
I have $3$ boxes - $B_1, B_2, B_3$. Each box initially contains a mixture of $3$ different kind of fruits say - Apple, Orange, Mango. Our goal is to arrange the fruits in the boxes in such a manner ...
- 101
0
votes
1
answer
1k
views
Finding number of subarrays not including certain pairs
How many contiguous subarrays of an array exist such that they do not contain certain pairs of positions of the array?
For eg. if array ={11,22,33,45}
and if we do not want to include say position ...
- 133
1
vote
0
answers
46
views
Number of ways to connect sets of k vertices in a perfect n-gon [duplicate]
This is a copy of my post at Mathexchange.com, as my question is still not fully answered and I really wanna find a solution to this. Feel free to refer to there for useful comments and partial ...
- 821
0
votes
1
answer
267
views
Permutation and Combination - Algorithm
Given Data in the problem
For I= 1 to 10
print(x)
means executing the immediate next line after for loop command 10 times. So here it prints "x" 10 times. Typical simple for loop construct in ...
- 1,717
0
votes
1
answer
4k
views
What is the meaning of ${}^n C_k \times {}^n P_k$?
I am trying to understand the bulls and cows document, Page $6$, equivalences.
Can someone please tell me what author means when he says
$\boldsymbol{ {}^n C_k \times {}^n P_k}$ like ${}^4 P_0 \...
- 101
3
votes
2
answers
3k
views
Sum of multiplication of all combination of m element from an array of n elements
Suppose I have an array {1, 2, 3, 4} and m = 3.
I need to find:
...
- 31
1
vote
1
answer
260
views
Catalan numbers with both prefix and suffix
In one of the applications of Catalan number,it calculates the number of Dyck word in which a string consisting of n $X's$ and n $Y's$ such that no prefix of the string has more $Y's$ than $X's$, and ...
- 303
1
vote
0
answers
822
views
Permutation for arranging letters in such a way that no similar letters come together (except SPACE)
I would like to get a general expression for arranging n letters such that any similar letters in them never come together (except SPACE).
For example :
Lets take AABBCCC and three spaces(...
3
votes
2
answers
246
views
Maximum number of seating plans
15 people will be seat in a row of 15 chairs.
Two seating plan are considered the same if
two plans share same adjacent quadruples.
What is the maximum number of seating plans can be made?
For ...
- 31
2
votes
1
answer
293
views
Counting permutations, with additional restrictions
There are 10 slots and some marbles: 5 red, 3 blue, 2 green, how many ways can you fit those marbles into those slots?
Those marbles fit in 10!/(5! 3! 2!) ways
...
- 404