Question

Suppose there are two bridges from Surrey to Burnaby and five roads from Burnaby to Coquitlam a. How many ways is it possible to travel from Surrey to Coquitlam via Burnaby b. How many different round-trip routes are there from Surrey to Burnaby to coyun Surrey ? c. How many different routes are there from Surrey to Rurnaby to Coquitlam to Burnaby and back to Sun which no road is traversed twice ? na-trip routes are there from Surrey to Burnaby to Coquitlam to Burnaby and back to Sol:

Answer 1

• a. There are 10 possible ways.
• b.There are 4 ways for a round trip
• c.There are 20 ways without repeating a road.
• d. There are 100 ways of doing a whole round trip.

a. For Surrey to Burnaby there are 2 ways and for Burnaby to Coquitlam 5, multiplying the available road gives us all the combinations.

b.From Surrey to Brunaby and back we have 2 ways going and 2 ways coming back. Multiplying gives us the 4 ways of doing the round trip.

c. If we don't want to repeat the road we will be using both bridges in Surrey to Brunaby beacause there are only 2 and we cant repeat one, and of the 5 avaliable from Burnaby to Coquitlam we will choose 2, that is, first 1 of 5 and then 1 of 4. Multiplying 5 times 4 gives us the ways of going and coming back without repeating.

d. For a whole round trip we choose from the bridges from Surrey to Brunaby twice, 2*2 and the roads from Burnaby to Coquitlam also twice, 5*5, giving us a total for a round trip of 100 different ways of doing it.