(i) Compute `2!+3!`. Is `2!+3!=5!` ?
(ii) Compute `(8!)/(4!)`. Is `(8!)/(4!)=2!` ?

Answer

Let's solve the given problems step by step.

### Part (i): Compute `2! + 3!`. Is `2! + 3! = 5!`?

1. **Calculate `2!`:**
\[ 2! = 2 \times 1 = 2 \]

2. **Calculate `3!`:**
\[ 3! = 3 \times 2 \times 1 = 6 \]

3. **Add `2!` and `3!`:**
\[ 2! + 3! = 2 + 6 = 8 \]

4. **Calculate `5!`:**
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]

5. **Compare `2! + 3!` with `5!`:**
\[ 8 \neq 120 \]

**Conclusion for Part (i):**
\[ 2! + 3! \text{ is not equal to } 5! \]

### Part (ii): Compute `(8!)/(4!)`. Is `(8!)/(4!) = 2!`?

1. **Calculate `8!`:**
\[ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]

2. **Calculate `4!`:**
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

3. **Write `(8!)/(4!)` as:**
\[ \frac{8!}{4!} = \frac{8 \times 7 \times 6 \times 5 \times 4!}{4!} \]

4. **Cancel `4!` in the numerator and denominator:**
\[ \frac{8!}{4!} = 8 \times 7 \times 6 \times 5 \]

5. **Calculate `8 \times 7 \times 6 \times 5`:**
- First, calculate \(8 \times 7 = 56\)
- Next, calculate \(56 \times 6 = 336\)
- Finally, calculate \(336 \times 5 = 1680\)

6. **Calculate `2!`:**
\[ 2! = 2 \times 1 = 2 \]

7. **Compare `(8!)/(4!)` with `2!`:**
\[ 1680 \neq 2 \]

**Conclusion for Part (ii):**
\[ \frac{8!}{4!} \text{ is not equal to } 2! \]

### Final Answers:
(i) \(2! + 3! \neq 5!\)
(ii) \(\frac{8!}{4!} \neq 2!\)

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