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IB Maths AA

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Permutations and combinations practice questions — IB Maths AA

11 free multiple-choice problems on permutations and combinations, ordered to match IB Maths AA difficulty, each with a full worked solution. No account needed — and there's a fresh problem set every day.

Try 3 problems from this chapter

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Problem #0410 International
Advancedcombinatorics
At a meeting, every pair of people shakes hands exactly once. If there are handshakes total, how many people are there?

Problems & worked solutions

Problem #0410 International

Problem 1 — Permutations and combinations

At a meeting, every pair of people shakes hands exactly once. If there are 45 handshakes total, how many people are there?

Show answer & worked solution
  1. A. 9
  2. B. 9.5
  3. C. 10✓ correct
  4. D. 45

n(n−1)2=45⇒n(n−1)=90⇒n=10.

Problem #0409 International

Problem 2 — Permutations and combinations

Using Pascal's identity (nk)+(nk+1)=(n+1k+1), compute (73)+(74).

Show answer & worked solution
  1. A. 35
  2. B. 56
  3. C. 70✓ correct
  4. D. 128

By Pascal: (73)+(74)=(84)=8!4! 4!=70.

Problem #0407 International

Problem 3 — Permutations and combinations

The number of two-digit numbers with distinct digits formable from {1,2,3,4,5} is:

Show answer & worked solution
  1. A. 10
  2. B. 20✓ correct
  3. C. 25
  4. D. 32

5⋅4=20, which is A52.

Problem #0404 International

Problem 4 — Permutations and combinations

The number of 3-letter codes that can be formed using letters from {A,B,C,D,E} without repetition is:

Show answer & worked solution
  1. A. 15
  2. B. 20
  3. C. 60✓ correct
  4. D. 125

A53=5⋅4⋅3=60.

Problem #0405 International

Problem 5 — Permutations and combinations

The number of 3-element subsets of a 5-element set is:

Show answer & worked solution
  1. A. 5
  2. B. 10✓ correct
  3. C. 15
  4. D. 60

(53)=5!3!⋅2!=10.

Problem #0406 International

Problem 6 — Permutations and combinations

Determine n∈N, n≥2, such that (n2)=15.

Show answer & worked solution
  1. A. 4
  2. B. 5
  3. C. 6✓ correct
  4. D. 15

n(n−1)2=15⇒n2−n−30=0⇒n∈{6,−5}. Only n=6 is admissible.

Problem #0408 International

Problem 7 — Permutations and combinations

The sum of all distinct three-digit numbers that can be formed using the digits {2,2,5} is:

Show answer & worked solution
  1. A. 522
  2. B. 774
  3. C. 999✓ correct
  4. D. 1220

The three distinct numbers are 225,252,522. Sum =225+252+522=999.

Problem #0402 International

Problem 8 — Permutations and combinations

The number of ways to arrange 4 distinct books on a shelf is:

Show answer & worked solution
  1. A. 4
  2. B. 16
  3. C. 24✓ correct
  4. D. 256

4!=24.

Problem #0403 International

Problem 9 — Permutations and combinations

A menu offers 4 appetizers, 5 mains, and 3 desserts. The number of distinct three-course meals is:

Show answer & worked solution
  1. A. 12
  2. B. 36
  3. C. 60✓ correct
  4. D. 120

4⋅5⋅3=60.

Problem #0401 International

Problem 10 — Permutations and combinations

The value of 5! is:

Show answer & worked solution
  1. A. 25
  2. B. 60
  3. C. 120✓ correct
  4. D. 720

5!=5⋅4⋅3⋅2⋅1=120.

1 more Permutations and combinations questions in the app

Also covered in Permutations and combinations practice across every exam.

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