Question

A sales representative can take one of 22 different routes from City Upper CCity C to...

A sales representative can take one of

22

different routes from

City Upper CCity C

to

City Upper ECity E

and any one of

77

different routes from

City Upper ECity E

to

City Upper MCity M.

How many different routes can she take from

City Upper CCity C

to

City Upper MCity M​,

going through

City Upper ECity E​?

solution:

Given Three cities are C , E and M

 CCity C ECity E MCity M

Step -1 : Sales representative moving from CCity C to ECity E

Given,

The total No.of different routes from  CCity C to ECity E = 22 [remember she may choose any one of the route]

Step -2 : Sales representative moving from ECity E to MCity M

The total No.of different routes from ECity E to MCity M = 77 [she may choose any one route ]

In first step she have 22 different routes through which she can pass to city E and there she have 77 ways to reach MCity M

Therefore,By product Rule:

Therefore,The Total No.of different routes she can take from CCity C to MCity M Through ECity E = 22 * 77 =1694