Combinatorics

Topic overview

Counting, the pigeonhole principle, recursion and probabilistic thinking.

Key concepts

Supplementary assessment for some colleges; currently available public sources are insufficient to confirm the paper structure on this site. For preparation training only; no claim is made that it is a current full mock paper.

Key points

◆Follow the prerequisite knowledge requirements given by the examination body; new concepts may only be used when the question provides sufficient guidance.
◆The examples on this site are training with a limited scope and do not represent full syllabus coverage or official difficulty.

Worked examples

Try each example yourself before checking the explanation.

1Written examples within the scope

How many binary strings of length 8 contain exactly three 1s?

How many contain no adjacent 1s?

Generalise to length n with exactly k non-adjacent 1s.

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