A chess team consisting of $2$ girls and $2$ boys is to be selected from the $7$ girls and $6$ boys in the chess club. Determine how many selections are possible if $2$ of the girls are twins and they must either both be included or both be excluded.
The digits in $1\,244\,687$ can be rearranged to form many different $7$-digit numbers. How many of these $7$-digit numbers are even?
How many different numbers in the range $20\,000$ to $30\,000$ can be made using $5$ distinct digits from the digits $1, 2, 4, 6, 7, 8$?
Helen has black tiles, white tiles and grey tiles. She arranges one row of $8$ tiles above her washbasin. Each tile she places is equally likely to be black, white or grey. Find the probability that no two adjacent tiles have the same colour.