# Combinations (How many combinations contain specific numbers)?

• term16
In summary, the conversation revolved around finding combinations of numbers and rearranging them into sets. The person first needed to find the combinations of 5 out of 35, which was determined to be 324632 combinations. They then wanted to fit these combinations into sets of 6 numbers and found that in theory, they could be rearranged into ~54.106 sets. However, they were unsure how to find out how many of these sets contained 5 specific numbers. It was also clarified that the decimal point in 324.632 was meant to represent thousands.
term16
I need to confirm something about combinations:

1. I need to find the combinations of 5 out of 35. <=> 35C5 = 324.632 combinations.
2. Now I want to try to "fit" these 324.632 combinations of five numbers into sets of 6 numbers. To do that, I first find how many combinations of five numbers is contained in a set of 6 numbers. ( 6C5=6). I then divide the 324.632 combinations by 6, which gives me 54105,333. So, in theory the 324.632 combinations of five could be rearranged into ~ 54.106 sets of 6 numbers.

Is that correct? And if so, how can I find out how many of the ~ 54.106 combinations contain 5 specific numbers?

no offense, but think about what you're saying. How can you have .632 of a combination?

if its combinations and order matters (i.e. a permutation), then you have 35!/(35-5!)

if its combinations and order doesn't matter (a combination), then you have 35!/[(35-5)!(5!)]

I know! I use the dot to separate thousands. It's not 324,632 , it's 324632! My question is how to "organize" or "rearrange" all the combinations of five numbers into combinations of six!

## 1. How do you calculate the number of combinations that contain specific numbers?

To calculate the number of combinations that contain specific numbers, you can use the formula nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items you want to choose. This formula is also known as the combination formula.

## 2. Can you provide an example of calculating combinations with specific numbers?

Sure, let's say we have a set of 6 numbers (1, 2, 3, 4, 5, 6) and we want to choose 3 numbers from this set. The number of combinations with specific numbers would be calculated as 6C3 = 6! / (3! * (6-3)!) = 20. So there are 20 different combinations that contain exactly 3 numbers from this set.

## 3. What if I want to calculate the number of combinations with specific numbers from a larger set?

If you want to calculate the number of combinations with specific numbers from a larger set, you can still use the same formula nCr = n! / (r! * (n-r)!). Just make sure to substitute the correct values for n and r in the formula.

## 4. How is the concept of combinations with specific numbers used in real life?

The concept of combinations with specific numbers is used in various fields such as statistics, probability, and computer science. It is used to calculate the number of possible outcomes in a given scenario, which can be helpful in making decisions and predictions.

## 5. Is there any other way to calculate combinations with specific numbers?

Yes, there are other ways to calculate combinations with specific numbers such as using a combination calculator or manually listing out all the possible combinations and counting them. However, the combination formula is the most efficient and accurate way to calculate the number of combinations.

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