Answer to Question #269441 in Combinatorics | Number Theory for sumu

Question

i) Kishan is a sales executive who has to make visits to Colombo, Kandy, Galle,

Gampaha, Panadura and Negombo. He has to visit each city once only and always

takes the unique shortest route between any two cities.

a. How many possible routes are there in total for his journey? (3 marks)

b. Kishan has been told he has to start his journey from Colombo. In this

scenario how many possible routes are there? (2 marks)

c. IfKishan was to pick a route for his entire journey for all six cities at

random, what is the probability that the route he selected would start from

Colombo? (3 marks)

d. Kishan's manager calls him and tells him there is not enough time to visit

every city and to choose only four. How many possible routes are there for

Kishan to take in this scenario?

Answer 1

a.

$$P(6, 6)=6!=720$$

b.

$$P(5, 5)=5!=120$$

c.

$$p=\dfrac{1}{6}$$

d. The order does not matter

$$C(6, 4)=\dbinom{6}{4}=\dfrac{6!}{4!(6-4)!}=\dfrac{6(5)}{1(2)}=15$$