Introduction:
The problem deals with the concept of probability in tossing a fair coin. We need to calculate the probability that the difference between the number of heads and tails is (n - 3).

Explanation:
To solve this problem, we can consider the following steps:

Step 1: Understanding the sample space:
When a fair coin is tossed, there are two possible outcomes - heads (H) or tails (T). Therefore, the sample space consists of 2^n possible outcomes since we are tossing the coin n times.

Step 2: Determining the favorable outcomes:
We need to find the probability that the difference between the number of heads and tails is (n - 3). Let's consider a scenario where the number of heads is (n - 3). In this case, the number of tails would be 3.

We can represent this scenario as follows:
HHH...HHH (n - 3 H's)
TTT (3 T's)

The number of ways to arrange (n - 3) H's and 3 T's can be calculated using the combination formula: C(n, n - 3) = C(n, 3) = nC3.

Step 3: Calculating the probability:
The probability of an event is given by the ratio of the favorable outcomes to the total number of outcomes. In this case, the favorable outcomes are nC3 and the total number of outcomes is 2^n.

Therefore, the probability can be calculated as:
P = nC3 / 2^n

Step 4: Simplifying the expression:
Using the formula for combination, nC3 = n! / (3!(n-3)!), we can simplify the expression as follows:

P = (n! / (3!(n-3)!) ) / 2^n
P = n! / (3!(n-3)! * 2^n)

Step 5: Analyzing the options:
Now, let's analyze the given options:
a) 2^-n
b) 0
c) nC(n-3)
d) 2^-n 3

Option 'b' states that the probability is 0. This is because when we simplify the expression, it does not contain any terms that can be canceled out with 2^n. Therefore, the expression cannot result in a probability of 0.

Conclusion:
Hence, the correct answer is option 'b' - 0. The probability that the difference between the number of heads and tails is (n - 3) is 0.