3.46: Digit arrangements and a binomial coefficient equation

Find how many different 5-digit numbers can be formed using the digits $1, 3, 5, 6, 8$ and $9$, with no digit used more than once.

How many of these 5-digit numbers are odd?

How many of these 5-digit numbers are odd and greater than $60\,000$?

Given that $45\times{}^{n}C_{4} = (n + 1)\,{}^{n + 1}C_{5}$, find the value of $n$.