# permutation problem 2

• Apr 26th 2009, 06:01 AM
wheresthecake
permutation problem 2
hey guys, need some help with this problem. this is one of four permutation problems that our teacher gave us to solve but haven't really figured it out, plus i was sick so i missed the lecture..
2) 4 routes lead from Town A to B and 3 from town B to O.

A: Find the no. of ways to travel from A to C via B
B: If a man wanted to travelroundtrip from A to C via B, how many ways are possible? Suppose he chooses a diff route, how many ways are possible?

thanks for the help. we've been given all the basic formula for permutations but I'm at a loss at how to apply them still.
• Apr 26th 2009, 09:05 PM
SengNee
Quote:

Originally Posted by wheresthecake
hey guys, need some help with this problem. this is one of four permutation problems that our teacher gave us to solve but haven't really figured it out, plus i was sick so i missed the lecture..
2) 4 routes lead from Town A to B and 3 from town B to C.

A: Find the no. of ways to travel from A to C via B
B: If a man wanted to travelroundtrip from A to C via B, how many ways are possible? Suppose he chooses a diff route, how many ways are possible?

thanks for the help. we've been given all the basic formula for permutations but I'm at a loss at how to apply them still.

A:
A to B: 4 $\displaystyle ^4C_1$
B to C: 3 $\displaystyle ^3C_1$

$\displaystyle ^4C_1 \cdot ^3C_1$

B:
Case I:
A to B: 4
B to C: 3
C to B: 3
B to A: 4

Case II:
A to B: 4
B to C: 3
C to B: 2 (cannot travel the same route as previous)
B to A: 3 (should travel the different routes)