Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Determine the number of arrangements of all $10$ letters in the word COPENHAGEN for which
(i)[3]

the vowels $(A, E, O)$ are grouped together and the consonants $(C, G, H, N, P)$ are grouped together.

(ii)[4]

the Es are not adjacent to one another.

(iii)[5]

Four letters are chosen from the $10$ letters of the word COPENHAGEN. Determine the number of different selections if the four letters are required to have the same number of Es and Ns, with at least one of each.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: A valid arrangement method, e.g. $(OAEE)(CPNHGN)$ or an equivalent one

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