Another type of listing involves sequential combinations; often known as the menu problem. This is a combination of possible items, followed by a further combination of possible items. If a burger bar was to offer a meal deal, it might offer:
This is tackled by working down each column in turn. Fix the frst two columns, and work down the third. When that is done, move the second column down one item, and work down the third column again. Finally, move the first column down one item, and repeat the whole process.
1. Alice is going to see her friend. She will either cycle or walk to the station. From the station she will take either a railway train or a bus. A the other end of this journey, she will either get a lift or take a taxi. How many combinations of transport could Alice take in going to see her friend?
There are 4 rows x 2 columns = 8 combinations.
C-Cycle W-Walk; B-Bus; R-Railway train, L-Lift, T-Taxi
2. Simon is writing a song. It will feature either a Drummer or a Bass player, but not both. It will also have either a Keyboards player, a Guitarist or a Singer. How many different combinations of instruments/singers could Simon have in his song?
and working through the combinations
3 rows x 2 columns = 6 combinations