Math CentralQuandaries & Queries


Question from Gary, a parent:

What is the number of possible combinations using the following fact pattern?
A. Each combination must have 4 numbers.
B. The possible numbers to choose from are 1, 2, 3, 4
C. The numbers can be included in the combination more than once. For example, it can be 1111.

Is it possible to generate a schedule of the possibilities?

Hi Gary,

Look at my response to Judy when she sent a similar question. She had 10 digits to choose from where you only have 4. In her case she had $10^6$ possibilities, too many to list. You have $4^4 = 256$ which is easier to deal with.

To list them start with 1111, then 1112, 1113 and 1114. Then 1121, 1122, 1123, 1124, 1131, and so on.

I hope this helps,

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