Quick questions on Permutations and combinations explained: H2 Mathematics Probability and Statistics

Arranging objects in a circle differs from a row, because rotating the whole circle does not create a new arrangement. Fixing one object's position removes this rotational duplication, so $n$ distinct objects arranged in a circle give $(n - 1)!$ arrangements rather than $n!$. For example, $5$ people around a round table can be seated in $(5 - 1)! = 4!

Many counting problems combine a combination and a permutation: first choose which objects, then arrange them. Because the two stages are independent, multiply the counts. To choose $3$ of $8$ books and then arrange them on a shelf, compute $\binom{8}{3} \times 3! = 56 \times 6 = 336$, which equals $^8P_3$ as a check.

Use the complement (total minus none) rather than adding overlapping cases.

How many ways can $6$ different people stand in a queue? [1 mark]

How many ways can a team of $3$ be chosen from $10$ players? [2 marks]

State whether choosing a president and a secretary from a club is a permutation or combination. [1 mark]