Lists can help solve problems. The type of list to be used depends upon the nature of the problem.
One type of listing deals with combinations.
To work out the various combinations of a number of different items, start with one item from the list. Make all the possible combinations from the remaining items in the list. Start a new column with a second item, and make all the possible combinations with the remaining items. Where possible, group combinations together.
How many possible combinations are there for the letters A, B, C and D?
Start the combinations in each column with a different letter. Work methodically through the combinations in alphabetical order.
| ABCD | BACD | CABD | DABC |
| ABDC | BADC | CADB | DACB |
| ACBD | BCAD | CBAD | DBAC |
| ACDB | BCDA | CBDA | DBCA |
| ADBC | BDAC | CDAB | DCAB |
| ADCB | BDCA | CDBA | DCBA |
Answer: 24
A train consists of a locomotive and three carriages. There is a first class carriage, a restaurant car and a standard class carriage. If the locomotive is always at the front, how many possible combinations are there for the train?
Use letters: F - First class; R - Restaurant; S - Standard class.
The Locomotive is always at the front, so it can be ignored.
| FRS | RFS | SRF |
| FSR | RSF | SFR |
Answer: 6