Eight railway stations A, B, C, D, E, F, G and H are connected either

1.	Eight railway stations A, B, C, D, E, F, G and H are connected either by two way passage or one way passages.One way passages are from C to A, E to G,B to F, D to H, G to C, E to C and H to G. Two way passagesare between A and E, G and B, F and D, and E and D.ques -While travelling from C to H, which one of the followingstations must be passed through.(a) G(b) E(c) B(d) F In how many different ways can a train travel from F to A without passing through any station more than once? (a) 1(b) 2(c)3(d)4
Answer» Given Total number of STATIONS = 8 Total number of passages = 2 ONE way PASSAGE = C to A, E to G,B to F, D to H, G to C, E to C and H to G Two way passage = between A and E, G and B, F and D, and E and D. To find: While travelling from C to H, which stations must be passed through. In how many different ways can a train travel from F to A without passing through any station more than once. Solution: One way passage CONNECTIONS - C-A, E-G, B-F, E-C, H-G, D-H, G-C Two way passages - A=E, G=B, E=D, F=D 1. If we want to travel from c to h there is only one possibility to go to A. From A only one to go to E. THUS, it needs to pass through E. 2. Following the path - F-D-E-C-A, F-D-H-G-C-A, F-D-E-G-C-A or F-D-E-A Thus total ways = 4

Eight railway stations A, B, C, D, E, F, G and H are connected either by two way passage or one way passages.One way passages are from C to A, E to G,B to F, D to H, G to C, E to C and H to G. Two way passagesare between A and E, G and B, F and D, and E and D.ques -While travelling from C to H, which one of the followingstations must be passed through.(a) G(b) E(c) B(d) F In how many different ways can a train travel from F to A without passing through any station more than once? (a) 1(b) 2(c)3(d)4

Answer»

Given

Total number of STATIONS = 8

Total number of passages = 2

ONE way PASSAGE = C to A, E to G,B to F, D to H, G to C, E to C and H to G

Two way passage = between A and E, G and B, F and D, and E and D.

To find:

While travelling from C to H, which stations must be passed through.

In how many different ways can a train travel from F to A without passing through any station more than once.

Solution:

One way passage CONNECTIONS -

C-A, E-G, B-F, E-C, H-G, D-H, G-C

Two way passages -

A=E, G=B, E=D, F=D

1. If we want to travel from c to h there is only one possibility to go to A.

From A only one to go to E. THUS, it needs to pass through E.

2. Following the path - F-D-E-C-A, F-D-H-G-C-A, F-D-E-G-C-A or F-D-E-A

Thus total ways = 4