USA Bus Lines

A math problem involving bus lines and finding the number of ways to take?

There are five bus lines from city A to city B and four bus lines from city B to city C. Find the number of ways a person can travel by bus. 1. Round trip from A to C by way of B 2. Round trip from A to C by way of B, without using a bus line more than once Thanks for the help, this problem is drivin me nuts

Public Comments

1. 1) Any of 5 buses from A to B, any of 4 buses from B to C. Return trip the same: 5*4*4*5 = 400 2) Any of 5 buses from A to B, any of 4 buses from B to c. Return trip, any bus but the one taken from C to B gives 3 choices, any but the one taken from B to A gives 4 choices. 5*4*(4 - 1)*(5 - 1) = 240
2. 1> well for round trip from a to c through b there are 5 ways to b from a and 4 ways to c from b so there are 5*4=20 ways to c from a through b so for round trip it is 20* 20=400 ways 2> for return path in second case we will have one less choice since it is already used in ato c path so we will have(5-1)*(4-1)=4*3=12 choices for return journey so we will have 20*12=240 ways when repetition is not allowed