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5 points, 5 arcs, names (II Soros Olympiad 1995-96 R2 10.3)

Source:

June 3, 2024

combinatorics

Problem Statement

Points

A

B

C

D

and

E

are placed on the circle. In how many ways can the resulting five arcs be designated by the letters

a

b

c

d

and

e

, if it is forbidden to designate an arc with the same letter as one of its ends? (For example, an arc with ends

A

and

B

cannot be designated by the letter

a

b