The first question is , the number of ways putting ten identical objects (in this case 1’s) into four different cells (in this case variables).

is the number of ways putting N identical objects into k different cells.

But in both of these cases some cells could be empty.

If we want no cell to be empty, we play a mind game.

Go ahead and put a 1 into each variable leaving 6 to distribute into the 4 variables.

This gives .

For the general case:

is the number of ways putting N identical objects into k different cells with no cell empty.