In the country abcd there are 17 roads from city a to city b. from city b to c −5 roads, from a to d −4 roads and from d to c −8 roads. how many ways can you drive from city a to city c?

117.

Step-by-step explanation:

In the country, ABCD are 4 cities.

Roads from city A to city B = 17

Roads from city B to city C = 5

Roads from city A to city D = 4

Roads from city D to city C = 8

We need to find the number of ways from city A to city C.

Route 1 : A-B-C

Total number of ways from A to B = C(17,1) = 17

Total number of ways from B to C = C(5,1) = 5

Total possible number of ways from A to C by route 1 is

A-B-C = 17 × 5 = 85

Route 2: A-D-C

Total number of ways from A to D = C(4,1) = 4

Total number of ways from D to C = C(8,1) = 8

Total possible number of ways from A to C by route 2 is

A-D-C = 4 × 8 = 32

Total ways to drive from city A to city C is

Therefore, the required number of ways is 117.