Evaluate (n - r) !, when :
(i) `n=6, r=2`
(ii) `n=9, r=5`

Answer

To evaluate \((n - r)!\) for the given values, we will follow these steps:

### Step 1: Evaluate \(n - r\) for the first case
Given:
- \(n = 6\)
- \(r = 2\)

Calculate:
\[ n - r = 6 - 2 = 4 \]

### Step 2: Calculate \( (n - r)! \) for the first case
Now we need to calculate \(4!\):
\[ 4! = 4 \times 3 \times 2 \times 1 \]

Calculating step-by-step:
- \(4 \times 3 = 12\)
- \(12 \times 2 = 24\)
- \(24 \times 1 = 24\)

Thus,
\[ (6 - 2)! = 4! = 24 \]

### Step 3: Evaluate \(n - r\) for the second case
Given:
- \(n = 9\)
- \(r = 5\)

Calculate:
\[ n - r = 9 - 5 = 4 \]

### Step 4: Calculate \( (n - r)! \) for the second case
Again, we need to calculate \(4!\):
\[ 4! = 4 \times 3 \times 2 \times 1 \]

As calculated previously:
- \(4 \times 3 = 12\)
- \(12 \times 2 = 24\)
- \(24 \times 1 = 24\)

Thus,
\[ (9 - 5)! = 4! = 24 \]

### Final Answers:
(i) \((6 - 2)! = 24\)
(ii) \((9 - 5)! = 24\)

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