113 There are three bridges connecting two towns A and B Bet

1.13. There are three bridges connecting two towns, A and B. Between towns B and C there arc four bridges. A salesperson has to travel from A to C via B. Find (a) the number of possible choices of bridges from A to C. (b) the number of Choices for a round-trip travel from A to C, and (c) the number of choices for a round-trip travel if no bridge is repeated.

Solution

(a)

Salesperson can travel from A to B in three ways and from B to C in 4 ways. Since path from A to B and from B to C are independent from each other. So the possible number of choices of bridges from A to C is

3*4=12

So required number of ways is 12.

(b).

Salesperson can travel from A to B in three ways and from B to C in 4 ways, then again from C to B in 4 ways and then from B to A in three ways. Since path from A to B and from B to C are independent from each other. So the possible number of choices of bridges for a round-trip travel from A to C is

3*4*4*3=144

So required number of ways is 144.

(c)

Salesperson can travel from A to B in three ways and from B to C in 4 ways, then again from C to B in 3 ways (leaving the used bridge when saleperson travel from B to C) and then from B to A in 2 ways (leaving the used bridge when saleperson travel from A to B). Since path from A to B and from B to C are independent from each other. So the possible number of choices of bridges for a round-trip travel from A to C, if no bridge is repeated, is

3*4*3*2=72

So required number of ways is 72.