# Thread: Total number of possible combinations?

1. ## Total number of possible combinations?

If there are 100 keys, each labeled with a number from 1 to 100, and a door that requires a combination of 25 keys (all in ascending order) to be opened, how many possible combinations of key sets are there?

You can not use the same key twice and each key set has to be in increasing order (key number 3, key number 7, key number 9, etc).

Thanks.

2. ## Re: Total number of possible combinations?

how many different combinations for a single door can be made?

or how many ways can you arrange the 100 keys to open 4 doors?

3. ## Re: Total number of possible combinations?

How many combinations for a single door, yes.

4. ## Re: Total number of possible combinations?

Originally Posted by Goobas
How many combinations for a single door, yes.
$\dbinom{100}{25} = 242519269720337121015504$

5. ## Re: Total number of possible combinations?

Thanks, i really appreciate it.