Combinations

The value of is

We use the property .

Therefore,

Alternatively, using Pascal's identity :

So the expression becomes

Answer: (A) 0

1. Understand the problem:

We need to evaluate the sum

2. Recall the combinatorial identity:

The key identity here is the "Hockey Stick Identity," which states:

This means that the sum of combinations of the form from to is equal to .

3. Apply the identity to the first five terms:

The sum can be written as:

Using the Hockey Stick Identity, this simplifies to:

4. Include the sixth term:

Now, add the sixth term to the result:

5. Simplify the expression:

The terms and cancel each other out, leaving:

6. Match the result to the options:

The simplified form corresponds to option (A).

Correct Answer: (A)