Q. There are seven dierent roads between town A and town B, four dierent roads b

Question

Q. There are seven dierent roads between town A and town B, four dierent roads between town B and town C, and two dierent roads between town A and town C.

(a) How many dierent routes are there from A to C altogether?
(b) How many dierent routes are there from A to C and back (any road can be used once in each direction)?
(c) How many dierent routes are there from A to C and back in part (b) that visit B at least once?
(d) How many dierent routes are there from A to C and back in part (b) that do not use any road twice?

Explanation / Answer

A -B 7 roads

B-C 4 roads

A-C 2 roads

a)no of dierent routes are there from A to C altogether = no of dierent routes from A to C directly +no of dierent routes from A to C through B = 2+ 7*4 = 30

b)no of dierent routes are there from A to C and back (any road can be used once in each direction) = no of dierent routes are there from A to C altogether*no of dierent routes are there from A to C altogether = 30*30 =900

c)no of dierent routes are there from A to C and back that visit B at least of dierent routes are there from A to C and back (any road can be used once in each direction) -no of dierent routes are there from A to C and back that don't touch not even once - 2*2 = 896

d)no of dierent routes are there from A to C and back that do not use any road twice =

no of dierent routes are there from A to C and back (any road can be used once in each direction)*(no of dierent routes are there from A to C and back (any road can be used once in each direction) -1 )

= 30*29 = 870

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