Thread: how many combinations if space is truncated

I know there are 7! combinations of the numbers 1 to 7.

But how many combinations of the numbers 1 to 7 are there if only five numbers are allowed. For example, if there are 7 people and only 5 chairs how many different combinations of seated people are there?


Thanks

Originally Posted by rainer

I know there are 7! combinations of the numbers 1 to 7.
But how many combinations of the numbers 1 to 7 are there if only five numbers are allowed. For example, if there are 7 people and only 5 chairs how many different combinations of seated people are there?

You are using the wrong word, combinations.
You seem to be talking about permutations.
A permutation has order but combinations have nothing to do with order.
The number of permutations of N objects taken k,

So

and