Combinations (How many combinations contain specific numbers)?

[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?

 

[ƒ(x)]

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!)]

 

[term16]

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!