Possible combinations of numbers?

In summary, the total number of possible combinations of numbers can be calculated using the formula nCr, where n is the total number of unique numbers and r is the number of numbers in each combination. To find all possible combinations of numbers without repetition, use the formula nPr. Combinations of numbers can be useful in science for various purposes, but there are limitations to finding them, such as computational intensity and potential repetitions.
  • #1
orangeincup
123
0

Homework Statement


Assuming 10 people pick a number between 1-120 and no two numbers can be the same, how many combinations of numbers can their be?

Homework Equations


C=N^s

The Attempt at a Solution


So I know the total possible for 120 would be just 120^10, but if I want to solve for the numbers never repeating in a sequence I'm not sure how.
 
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  • #2
The first guy picks one number from 1 to 120. So he has 120 choices. But the second guy has 119 choices because one number is taken by the first guy. Similarly the third guy has 118 choices. And so on.
 

1. What is the total number of possible combinations of numbers?

The total number of possible combinations of numbers can be calculated using the formula nCr, where n is the total number of unique numbers and r is the number of numbers in each combination. For example, if you have 10 unique numbers and want to find all possible combinations of 3 numbers, the formula would be 10C3 = 120. So, there are 120 possible combinations of 3 numbers from a set of 10 unique numbers.

2. How do you find all possible combinations of numbers without repetition?

To find all possible combinations of numbers without repetition, use the formula nPr, where n is the total number of unique numbers and r is the number of numbers in each combination. For instance, if you have 10 unique numbers and want to find all possible combinations of 3 numbers without repetition, the formula would be 10P3 = 720. So, there are 720 possible combinations of 3 numbers without repetition from a set of 10 unique numbers.

3. Can you give an example of possible combinations of numbers?

Sure, let's say we have a set of 4 unique numbers: 1, 2, 3, and 4. The possible combinations of 3 numbers from this set would be: 123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432.

4. How can combinations of numbers be useful in science?

Combinations of numbers can be useful in science for various purposes, such as generating random samples for experiments, creating unique sequences for genetic studies, and creating unique identifiers for data analysis. They can also be used to calculate probabilities and predict outcomes in statistical analyses.

5. Are there any limitations to finding possible combinations of numbers?

Yes, there are limitations to finding possible combinations of numbers. As the number of unique numbers and the number of numbers in each combination increase, the total number of combinations also increases exponentially. This means that it can become computationally intensive to find all possible combinations for large sets of numbers. Additionally, if there are repetitions allowed in the combinations, the total number of combinations will be even greater.

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