How many Permutations and combinations questions are there for 9709?

This page collects 12 recent Cambridge Mathematics (9709) past-paper questions tagged to Permutations and combinations. Each links straight to instant marking against the official 9709 scheme.

How are Permutations and combinations answers marked?

Type or photograph your working and MarkScheme scores it against the real 9709 mark scheme for this topic — method, accuracy and any band descriptors — so you see exactly where the marks are.

Where can I learn Permutations and combinations first?

Start with the free Mathematics lesson on Permutations and combinations, then come back and drill past-paper questions under timed conditions.

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9709 · topic questions

Permutations and combinations

Mathematics12 questions

12 past-paper questions on Permutations and combinations

9709/52 · May/June 20245 marks
Find the probability that a randomly chosen arrangement of the 10 letters in the word REGENERATE is one in which the consonants…
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9709/52 · May/June 20244 marks
How many different arrangements are there of the 10 letters in the word REGENERATE in which the 4 Es are together and the 2 Rs…
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9709/51 · May/June 20254 marks
Find the number of different ways in which the 6 musicians can be selected if there must be at least 3 guitarists, at most 2…
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9709/52 · October/November 20244 marks
On another occasion a group of 5 will be chosen from the 21 students. The group must contain at least 2 violinists, at least 1…
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9709/51 · May/June 20244 marks
Find the number of different arrangements of the 8 digits in which there is a 2 at the beginning, a 2 at the end and the three 4s…
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9709/51 · October/November 20244 marks
Four letters are selected at random from the 9 letters in the word INTELLECT. (c) Find the percentage of the possible selections…
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9709/51 · October/November 20243 marks
How many different arrangements are there of the 9 letters in the word INTELLECT in which there is a T at each end and the two Es…
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9709/51 · May/June 20253 marks
Find the number of different arrangements of the 8 letters in the word KANGAROO in which the two As are together and the two Os…
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9709/51 · May/June 20253 marks
Three bands will be selected from the original group of 20 musicians. Each band will consist of 3 guitarists, 1 pianist and 1…
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9709/52 · May/June 20253 marks
Find the number of different ways in which the 10 letters in the word AMALGAMATE can be arranged so that there is an M at the…
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9709/52 · May/June 20253 marks
Find the number of different ways in which the 10 letters in the word AMALGAMATE can be arranged with exactly 3 letters between…
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9709/52 · May/June 20253 marks
Five letters are selected from the 10 letters in the word AMALGAMATE. Find the number of different selections in which the five…
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Question stems are shortened previews. Open a question to attempt the full version and have it marked.

Worked example

What a lost mark actually looks like

This answer reaches the right coordinates and still drops a mark — the conclusion is stated, but never justified. Examiners pay for the reasoning, not the answer.

MARKED

80%

Strong

M1dy/dx = 3x^2 - 12x + 9M1 earned
M1(x - 1) $(x - 3) = 0$ M1 earned
A1 $x = 1$ or $x = 3$ A1 earned
B1(1, 5) is a maximum and (3, 1) is a minimumB1 not earned

B1 — withheld
You stated the nature of each point correctly, but stated it without justification. This mark needs the reasoning shown — either evaluate the second derivative (d²y/dx² = 6x − 12, giving −6 at $x = 1$ and +6 at $x = 3$ ) or show a sign change of dy/dx either side of each point. An unsupported assertion earns nothing here even when the conclusion is right.

Permutations and combinations (9709) past-paper questions — marked instantly

These are real Cambridge Mathematics past-paper questions on Permutations and combinations. Open one, attempt it, then upload your working — MarkScheme grades it against the official 9709 mark scheme so you see exactly where the marks are won and lost on this topic.

Mark your answer →Learn Permutations and combinations 9709 grade boundaries

Frequently asked questions

How many Permutations and combinations questions are there for 9709?: This page collects 12 recent Cambridge Mathematics (9709) past-paper questions tagged to Permutations and combinations. Each links straight to instant marking against the official 9709 scheme.
How are Permutations and combinations answers marked?: Type or photograph your working and MarkScheme scores it against the real 9709 mark scheme for this topic — method, accuracy and any band descriptors — so you see exactly where the marks are.
Where can I learn Permutations and combinations first?: Start with the free Mathematics lesson on Permutations and combinations, then come back and drill past-paper questions under timed conditions.