# Thread: how many combinations if space is truncated

1. ## 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

2. ## Re: how many combinations if space is truncated

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, $\displaystyle _N\mathcal{P}_k=\frac{N!}{(N-k)!}$

So $\displaystyle _7\mathcal{P}_7=\frac{7!}{(0)!}=7!$

and $\displaystyle _7\mathcal{P}_5=\frac{7!}{(2)!}=7\cdot 6\cdot 5\cdot 4\cdot 3$