AS Level · Mathematics 9709 · Probability & Statistics 1

Permutations & combinations: AS Level Mathematics questions with answers

Free Permutations & combinations questions for AS Level Mathematics (9709), part of Probability & Statistics 1. Each question has the answer and the marking points an examiner would look for.

Generate a full Permutations & Combinations worksheet →All Probability & Statistics 1 questions

Permutations & combinations practice questions

Question 1Structured · 8 marksA* challenge

This question is about arrangements of the 8 letters of the word PARALLEL.

(a)

Find the number of different arrangements of the letters.

[1]
(b)

Find the number of different arrangements in which all the vowels are together.

[3]
(c)

Find the number of different arrangements in which no two vowels are next to each other.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)3360
3360 B1
1
(b)360
treat the vowels as one unit M1
multiply by arrangements of the vowels within the unit, dividing for repeats M1
360 A1
3
(c)1200
arrange consonants: 20 B1
choose 3 of the 6 gaps: 20 M1
arrange vowels: 3 M1
1200 A1
4
Question 2Structured · 6 marksA* challenge

A committee of 5 people is to be chosen from 8 men and 5 women.

(a)

Find the number of different committees with at least 2 women.

[3]
(b)

Mr Khan and Ms Lee refuse to serve together. Find the number of committees with at least 2 women that do not include both of them.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)881
consider separate cases by number of women M1
at least two cases correct A1
881 A1
3
(b)751
subtract committees containing both M1
130 with both A1
751 A1
3
Question 3Structured · 2 marks

Find the number of different arrangements of the 7 letters in the word BANANAS.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
420
7! ÷ (3! × 2!) M1
420 A1
2
Question 4Structured · 8 marksA* challenge

This question is about arrangements of the 9 letters of the word STATISTIC.

(a)

Find the number of different arrangements of the letters.

[1]
(b)

Find the number of different arrangements in which all the vowels are together.

[3]
(c)

Find the number of different arrangements in which no two vowels are next to each other.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)15120
15120 B1
1
(b)1260
treat the vowels as one unit M1
multiply by arrangements of the vowels within the unit, dividing for repeats M1
1260 A1
3
(c)6300
arrange consonants: 60 B1
choose 3 of the 7 gaps: 35 M1
arrange vowels: 3 M1
6300 A1
4
Question 5Structured · 6 marksA* challenge

A committee of 6 people is to be chosen from 8 men and 5 women.

(a)

Find the number of different committees with at least 2 women.

[3]
(b)

Mr Khan and Ms Lee refuse to serve together. Find the number of committees with at least 2 women that do not include both of them.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)1408
consider separate cases by number of women M1
at least two cases correct A1
1408 A1
3
(b)1113
subtract committees containing both M1
295 with both A1
1113 A1
3
Question 6Structured · 2 marks

Find the number of different arrangements of the 7 letters in the word SUCCESS.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
420
7! ÷ (3! × 2!) M1
420 A1
2

More Probability & Statistics 1 questions

Representation of dataProbability & the binomial distributionDiscrete random variablesThe normal distribution

Want a mentor, not just a paper?

Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.

Meet Riyaz →

Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in