Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) 15.) Consider the regular hexagon shown. (a) In how many ways can the vertices be labelled with a distinct letter of the alphabet? (b) How many different triangles can be formed inside the hexagon by connecting 3 of the vertices? (c) In how many ways can the vertices be labelled with a distinct letter of the alphabet if the top right vertex must be labelled P or Q, and three of the other letters must be A,B,C ?

Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) 15.) Consider the regular hexagon shown. (a) In how many ways can the vertices be labelled with a distinct letter of the alphabet? (b) How many different triangles can be formed inside the hexagon by connecting 3 of the vertices? (c) In how many ways can the vertices be labelled with a distinct letter of the alphabet if the top right vertex must be labelled P or Q, and three of the other letters must be A,B,C ?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Note: In this problem set, the notation C(n, k) is used for
the combination "n choose k." Alternate notation: ( )

15.) Consider the regular hexagon shown.
(a) In how many ways can the vertices be labelled with a distinct letter of the
alphabet?
(b) How many different triangles can be formed inside the hexagon by
connecting 3 of the vertices?
(c) In how many ways can the vertices be labelled with a distinct letter of the alphabet if the top
right vertex must be labelled P or Q, and three of the other letters must be A,B,C ?

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