How Many Dominoes in a Double-Nine Set?
A standard double-nine domino set contains a total of 55 dominoes. This isn't just a random number; it's a result of mathematical combinations. Let's explore why.
Understanding the Dominoes
Each domino tile is characterized by two numbers (or pips) ranging from 0 to 9. A double-nine set includes all possible combinations of these numbers, where the order doesn't matter (a 2-5 is the same as a 5-2).
The Calculation
To calculate the number of dominoes, we can use a mathematical concept called combinations. Specifically, we need to find the number of combinations of selecting two numbers (with replacement) from a set of ten numbers (0 through 9). The formula for combinations with replacement is:
(n + k - 1)! / (k! * (n - 1)!)
Where:
- 'n' is the number of items to choose from (in this case, 10 numbers: 0-9).
- 'k' is the number of items chosen at a time (in this case, 2, since each domino has two numbers).
Plugging in our values:
(10 + 2 - 1)! / (2! * (10 - 1)!) = 11! / (2! * 9!) = (11 * 10) / (2 * 1) = 55
Therefore, there are 55 unique dominoes in a double-nine set.
Why 55? A Simpler Explanation
You can also think of it this way:
- Doubles: There are 10 double dominoes (0-0, 1-1, 2-2, and so on, up to 9-9).
- Non-Doubles: For each number, there are 9 non-double combinations. Since there are 10 numbers, this gives us 10 * 9 = 90 combinations. However, we've double-counted each combination (like 2-5 and 5-2), so we divide by 2 to get 45.
Adding the doubles and non-doubles together: 10 + 45 = 55
What About Other Domino Sets?
The same principle applies to other sets. For example:
- Double-six: (6 + 2 - 1)! / (2! * (6 - 1)!) = 28 dominoes
- Double-twelve: (12 + 2 - 1)! / (2! * (12 - 1)!) = 91 dominoes
This understanding of combinations allows you to easily calculate the number of dominoes in any double-n set.
Are there any variations in domino sets?
While the standard double-nine set is most common, you might occasionally find variations in the size or design of the dominoes themselves. However, the number of dominoes within a standard set remains consistent at 55.
This comprehensive explanation should answer all your questions about the number of dominoes in a double-nine set. Remember, the key is understanding the mathematical combinations involved!
