In how many ways you can triangulate a simple polygon with n vertices. Give both qualitative...

In how many ways you can triangulate a simple polygon with n vertices. Give both qualitative and quantitative answer.

Expert Solution

Colby Messinger answered 1 year ago

Simple answers but work shown thank you! (a) In how many different ways can the letters...

Simple answers but work shown thank you! (a) In how many different ways can the letters of the word wombat be arranged? (b) In how many different ways can the letters of the word wombat be arranged if the letters wo must remain together (in this order)? (c) How many different 3-letter words can be formed from the letters of the word wombat? And what if w must be the first letter of any such 3-letter word?

(a) What is the maximum degree of a vertex in a simple graph with n vertices?...

(a) What is the maximum degree of a vertex in a simple graph with n vertices? (b) What is the maximum number of edges in a simple graph of n vertices? (c) Given a natural number n, does there exist a simple graph with n vertices and the maximum number of edges?

In how many ways n distinct balls can be given to k children so that no...

In how many ways n distinct balls can be given to k children so that no child gets more than 3 balls?

a) In how many ways n distinct ball can be given to k children so that...

a) In how many ways n distinct ball can be given to k children so that no child gets more than 3 balls? b) What happens if the balls are indistinguishable?

Let G be a simple undirected graph with n vertices where n is an even number....

Let G be a simple undirected graph with n vertices where n is an even number. Prove that G contains a triangle if it has at least (n^2 / 4) + 1 edges using mathematical induction.

In how many ways can you arrange the letters of " ARRANGEMENT?"

Q 4 One can think of a circle as an N-sided polygon where N is a...

Q 4 One can think of a circle as an N-sided polygon where N is a very very large number. This is because as the number of sides of a polygon increases the shape of the polygon starts resembling that of a circle. In the light of this fact explain why the diffraction pattern produced by the aperture DOTS is made of alternating bright and dark circular bands. Hint: First determine the diffraction pattern produced by an N-sided polygon. Then...

Consider an undirected graph G that has n distinct vertices. Assume n≥3. How many distinct edges...

Consider an undirected graph G that has n distinct vertices. Assume n≥3. How many distinct edges will there be in any circuit for G that contains all the vertices in G? What is the maximum degree that any vertex in G can have? What is the maximum number of distinct edges G can have? What is the maximum number of distinct edges that G can have if G is disconnected?

In how many ways can you arrange 5 books in a bookshelf?

In how many ways can you arrange 5 books in a bookshelf? Give details

Show that the number of labelled simple graphs with n vertices is 2n(n-1)/2. (By induction way!)

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