Permutations and Combinations

May 2010
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A travel agent is trying to schedule a client's trip from city A to city B. There are 3 direct flights, 3 flights from A to a connecting city C, and 4 flights from the connecting city C to city B. How many trips are possible?

do you just multiply 3*3*4?

 

Soroban

MHF Hall of Honor
May 2006
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Lexington, MA (USA)
Hello, hahaitssara!

A travel agent is trying to schedule a client's trip from city A to city B.
There are 3 direct flights from city A to city B.
There are: 3 flights from city A to city C, and 4 flights city C to city B.

How many trips are possible?

There are two possible scenarios:

. . \(\displaystyle A\quad \longrightarrow \quad B\) . . . . . . . . . 3 trips
. . . . \(\displaystyle ^{\text{3 flights}}\)

. . \(\displaystyle A\quad\longrightarrow\quad C \quad\longrightarrow \quad B \). . 12 trips
. . . . \(\displaystyle ^{\text{3 flights} } \qquad\;\; ^{\text{4 flights}}\)


\(\displaystyle \text{Therefore, there are: }\;3 + 12 \:=\:15\,\text{ possible trips.}\)

 
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Dec 2009
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A travel agent is trying to schedule a client's trip from city A to city B. There are 3 direct flights, 3 flights from A to a connecting city C, and 4 flights from the connecting city C to city B. How many trips are possible?

do you just multiply 3*3*4?

Hi Sara,

It depends on the times of the flights to and from the connecting town B.
In other words, if all 4 flights from B to C leave after the last flight from A arrives at B,
then you can include all 12 possibilities with the 3 direct flights from A to C.