If There Are 3 Roads From Town A To Town B And 4 Roads From Town B To Town C. How Many Way…

if there are 3 roads from Town A to Town B and 4 roads from Town B to Town C. How many ways can one go from Town A to C and back to Town A through the Town B without passing through the same road twice?

This problem can be solved using the Fundamental Principle of Counting or FPC. The FPC states that if one event can be done in [tex]m[/tex] ways and another event can be done in [tex]n[/tex] ways, the number of ways that the two events can happen is [tex]mn[/tex] ways. For example, if you have 2 different shirts and 5 different pair of pants, the number of possible combinations of a shirt and a pair pants that you can make is  2×5 = 10 ways.

Now, to solve this problem, we have to remember that the route is this: From A to B, then from B to C, then from C back to B, and from B back to A. 

Let’s count our choices:
(a) From A to B, we have 3 roads to choose from;
(b) From B to C, we have 4 roads to choose from;
(c) In going back from C to B, we only have 3 options this time since we already took one in (b), again we cannot take the same road twice;
(d) From B to A, we only have 2 roads to choose from since we already took one in (a).

Therefore, applying the FPC now, we have a total of 3×4×3×2 = 72 ways.

See another problem that uses FPC: brainly.ph/question/279814

garden city centre welwyn village housing gardens shopping lined boulevards brick demand properties along houses built those tree modern most

What is a garden village and would you welcome one nearby?. Tripadvisor west community side garden. City westfield

Ang mo kio town garden west, singapore. Garden city centre welwyn village housing gardens shopping lined boulevards brick demand properties along houses built those tree modern most. City westfield

West side community garden (new york city). West side community garden. Ang mo kio town garden west ความสงบแห่งเมืองอังโมเกียว (ที่เที่ยว

esh

Ang mo kio town garden west ความสงบแห่งเมืองอังโมเกียว (ที่เที่ยว. Community garden west side tripadvisor. Kio ang mo garden west town singapore eventfinda tweet list

tracysnewyorklife

City garden in south west london – bowles & wyer. City west place garden. A three-year renovation and a glass rooftop studio perfect this $26m

Village west garden. Town garden overview. Sudafrica guida

tripadvisor west community side garden

West garden. Community garden west side tripadvisor. West_park_garden_village_header_image_1

geograph

Garden city. Saga seeds picking @ ang mo kio town garden west. Tripadvisor west community side garden

garden west ang kio mo town saga seeds picking valentine idea gift childhood brought remembered fond memories come lot really

West side community garden (new york city). What is a garden village and would you welcome one nearby?. Ang mo kio garden mcdonald

Matt keightley; ogród nowoczesny symetryczny. Kio ang mo town garden saga seeds picking west valentine idea gift reach steps race because another would just. Town garden overview

west community side garden tripadvisor

This upper west side community garden is a neighborhood hub. it boasts. Village west garden. West side community garden (new york city)

town garden overview

West side community garden (new york city). Town garden overview. Garden route, sudafrica: guida ai luoghi da visitare