How to Calculate Possible Combinations in Dominoes

Written by michael keenan | 13/05/2017
How to Calculate Possible Combinations in Dominoes
Dominoes with the same number on each side are known as doubles. (dominoes image by Paul Heasman from

Dominoes is a game that uses tiles with two sections, each containing between zero and six dots. You can play your tiles next to other tiles that have the same number of dots on one half. To calculate the number of possible combinations in dominoes, use the formula for combinations where order does not matter and repetition is allowed. Because order does not matter, a domino with three dots on one side and two dots on the other is the same as a domino with two dots on one side and three dots on the other. Repetition being allowed means that you can have a domino with the same number of dots in both boxes.

Determine the amount of numbers you could end up with on each side of the domino and call this N. Since each square can have from zero to six dots, there are seven possible combinations, so N will be 7.

Set R equal to 2 because there are two boxes for dots on each domino.

Add N plus R minus 1 to get 8.

Calculate the factorial of the result from Step 3. Factorial, notated with !, requires you to multiply the number by each of the positive integers less than it. For example, 4! would equal 4x3x2x1. For dominoes, you would calculate 8! to get 40,320.

Subtract one from N and take the factorial of the result. For dominoes, you would subtract 1 from 7 get 6 and then calculate 6! to get 720.

Multiply the result from Step 5 by R!. For dominoes, R equals 2 and 2! equals 2, so you would multiply 720 by 2 to get 1,440.

Divide the result from Step 4 by the result from Step 6 to calculate the number of combinations. For dominoes, you would divide 40,320 by 1,440 to find that there are 28 possible combinations for dominoes.

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