Hello, veronicak5678!

I hope I understand the problem . . .

Suppose you want to choose a -element subset

from the -element set: .

You do this by choosing first the middle element,

then elements from its left,

then elements from its right.

Formulate the combinatorial identity you get from doing this.

The question could have been stated more clearly.

Since there is a "middle element", I assume that is odd.

Then the middle element is

There are: elements to the left, and elements to the right.

We select the middle element: 1 way.

We select elements from the elements on the left.

. . There are: . ways.

We select elements from the elements on the right.

. . There are: . ways.