The range of the function `f(x)=\ ^(7-x)P_(x-3)` is (a) {1, 2, 3, 4, 5} (b) {1, 2, 3, 4, 5, 6} (c) {1, 2, 3, 4} (d) {1, 2, 3}

Explanation

To find the range of the function \( f(x) = \ ^{(7-x)}P_{(x-3)} \), we will follow these steps:

### Step 1: Understand the permutation formula
The permutation formula is given by:
\[ ^nP_r = \frac{n!}{(n-r)!} \]
In our case, \( n = 7 - x \) and \( r = x - 3 \). Therefore, we can rewrite the function as:
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