There are 56 possible combinations for promotion.

Now to see how this arises, let's do a simpler case.

Where we can count up all the individual possibilities.

What if there were only three surveyors, and there were two possible slots?

Or two possible ways to arrange them.

Then, in that case, our three surveyors are labeled A, B, C.

And you see there are only three different combinations of those that we can make.

Either AB, AC or BC.

So the answer is going to be three.

Now, note that BA is not a separate combination.

Because in this case there's a combination, the order doesn't matter.

So AB and BA are not separate combinations.

And there are only, in this case, three available, as here.

Well, does the equation agree with that?

So in this case, again the same general equation applies here for C and R.

But now N is equal to three, and R is equal to two.

So that is equal to the expression here.

Which expanding it out is equal to that.

And the answer is three.

So indeed we can see that this is correct.