Find the value of n such that
` "(i) "^(n)P_(5) =42 xx ""^(n)P_(3), n gt 4 " (ii) "(""^(n)P_(4))/(" "^(n-1)P_(4))=(5)/(3), n gt 4.`

Explanation

To solve the given problems step by step, we will break down each part of the question.

### Problem (i):
We need to find \( n \) such that \( ^{n}P_{5} = 42 \times ^{n}P_{3} \).

1. **Write the formula for permutations**:
\[
^{n}P_{r} = \frac{n!}{(n-r)!}
...