IIMB 2002 (QA) PYQs

The number of ways of selecting two numbers $a$ and $b$, $a$ $\in \{ 2,4,6, \cdots,100\}$ and $\mathrm{b} \in\{1,3,5, \ldots, 99\}$ such that $2$ is the remainder when $\mathrm{a}+\mathrm{b}$ is divided by $23$ is

How many numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?

A person hosts a party of 13 guests and places 5 of them on one table and the remaining on the other table, the tables being round. In how many ways can he arrange the guests?