Math CentralQuandaries & Queries


Question from Nancy:

Good evening. I'm in a quandary. Can you help? I would like to know what 4-digit combinations can be derived from 1-3-4-8-0 no repetitions

Hi Nancy,

Selecting four digits from 1, 3, 4, 8, and 0 is equivalent to selecting one digit not to include. There are 5 digits to choose from to select the one not to include and hence there are five ways to choose 4 digit from 1, 3, 4, 8, and 0. You can list them. they are


This assumes that order is not important, that is 3,4,8,0 and 4,3,8,0 are equivalent. If order is important then each of the five selection listed above can be ordered in 24 different ways. For example if you have the four digits 3,4,8,0 then you can choose which of them to list first in 4 different ways, 3,4,8 or 0. Once you have chosen which digit to list first there are 3 choices for the second digit. Hence there are $4 \times 3$ ways to order the first two digits. Again, once you have chosen the first two digits there are 2 possibilities for the third digit. Hence there are $4 \times 3 \times 2$ ways to order the first three digits. At this point there is only one choice for the last digit and hence there are $4 \times 3 \times 2 \times 1$ ways to order all four digits.

Write back if you need further assistance,

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