IB · Mathematics: Analysis & Approaches SL & HL · Number & algebra

Counting principles: IB Mathematics: Analysis & Approaches questions with answers

Free Counting principles questions for IB Mathematics: Analysis & Approaches (SL & HL), HL only, part of Number & algebra. Each question has the answer and the marking points an examiner would look for.

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Counting principles practice questions

Question 1Structured · 6 marksA* challenge

A committee of 5 people is chosen from 8 men and 4 women.

(a)

Find the number of committees that contain at least two women.

[3]
(b)

Two particular people refuse to serve on the committee together. Find the number of possible committees.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)456
total 12C5 = 792 (A1)
subtract committees with 0 or 1 woman: 56 + 280 (M1)
456 A1
3
(b)672
committees containing both: 10C3 = 120 (A1)
792 − 120 (M1)
672 A1
3
Question 2Structured · 6 marks

Consider the 8 letters of the word ADDITION.

(a)

Find the number of different arrangements of these 8 letters.

[2]
(b)

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

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)10080
8!2! 2! (M1)
10080 A1
2
(b)720
treat the vowels as a single block (M1)
arrangements of the block and 4 consonants: 60 (A1)
arrangements within the block: 12 (A1)
720 A1
4
Question 3Structured · 6 marksA* challenge

A committee of 4 people is chosen from 5 men and 4 women.

(a)

Find the number of committees that contain at least two women.

[3]
(b)

Two particular people refuse to serve on the committee together. Find the number of possible committees.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)81
total 9C4 = 126 (A1)
subtract committees with 0 or 1 woman: 5 + 40 (M1)
81 A1
3
(b)105
committees containing both: 7C2 = 21 (A1)
126 − 21 (M1)
105 A1
3
Question 4Structured · 6 marks

Consider the 8 letters of the word PARALLEL.

(a)

Find the number of different arrangements of these 8 letters.

[2]
(b)

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

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)3360
8!2! 3! (M1)
3360 A1
2
(b)360
treat the vowels as a single block (M1)
arrangements of the block and 5 consonants: 120 (A1)
arrangements within the block: 3 (A1)
360 A1
4
Question 5Structured · 6 marksA* challenge

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

(a)

Find the number of committees that contain at least two women.

[3]
(b)

Two particular people refuse to serve on the committee together. Find the number of possible committees.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)881
total 13C5 = 1287 (A1)
subtract committees with 0 or 1 woman: 56 + 350 (M1)
881 A1
3
(b)1122
committees containing both: 11C3 = 165 (A1)
1287 − 165 (M1)
1122 A1
3
Question 6Structured · 6 marks

Consider the 8 letters of the word SYMMETRY.

(a)

Find the number of different arrangements of these 8 letters.

[2]
(b)

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

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)10080
8!2! 2! (M1)
10080 A1
2
(b)10080
treat the vowels as a single block (M1)
arrangements of the block and 7 consonants: 10080 (A1)
arrangements within the block: 1 (A1)
10080 A1
4

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in