Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

(a)[3]

Determine how many distinct arrangements of the 10 letters in AMALGAMATE there are when an M is at the start, another M is at the end, and no As are adjacent.

(b)[3]

Determine how many distinct arrangements of the 10 letters in AMALGAMATE there are with exactly 3 letters between the two Ms.

(c)[3]

Select five letters from the 10 letters in the word AMALGAMATE. Find the number of different selections in which the five letters contain at least one M and at least two As.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A valid counting approach for arrangements with the given restrictions, such as $4!\times {}^{5}C_{1}$ or an equivalent expression.” …

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