## math for fun

## Forum Posts

Βασίλης Κέκεσης

May 19, 2022

In Math Problems

Hey guys I have a probability problem that I can not solve. In the problem we have 10 boys and 5 girls. We take all of them(15 people) and we place them next to each other(in a row). What is the probability that at least 1 girl is placed next to another girl? At first I thought it would be easier to find the possibility that there is no girl placed next to another girl so the original possibility I am asked to find will be 1 minus this possibility. However I sill find it difficult to solve.

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Βασίλης Κέκεσης

Dec 20, 2020

In Math Problems

Hello, some of you might have heard of this problem before. A salesman is at the starting point of N cities and wants to visit the remaining (N-1) cities of a network and return to the starting point by travelling the minimum distance. Each city is visited only once. Usually a table with the distance between the cities is given. For example, for N = 7 the following table is given: Basically, this is a linear programming problem that can be solved with the Miller ,Tucker and Zemmlin formulation, which is the following: I understand that the 1nd constraint is to require that each city is arrived at from exactly one city and the 2nd is to require that from each city there is a departure to exactly one other city. However, I don't understand what the 3rd constraint wants to show. I would appreciate if anyone could explain and write down how this constraint is applied to the problem above.

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Βασίλης Κέκεσης

May 24, 2020

In Math Problems

can someone explain me step by step solution to the following integral? Wolphram Alfa says the answer is 288000

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Βασίλης Κέκεσης

May 18, 2020

In Math Problems

yz-λy-λz=0 xz-λx-λz=0 xy-λx-λy=0 xy+xz+yz=150 I have to solve for x,y,z,λ

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