Permutations and Combinations · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
به انگلیسی

Order matters, or it does not

Mathematics · Discrete Mathematics · ages 18-19
Name ______________________   Date ____________

  1. Five runners compete for one gold and one silver medal. There are no ties, and nobody can win both. How many medal outcomes are possible?

    Answer: ______________

  2. Choose 2 different books from A, B, C, D and E for a loan. Book A must be included. Order does not matter. How many loans are possible?

    Answer: ______________

  3. A reader chooses 3 different books for one loan. Their order on the form has no effect. Which count fits?

    • A combination: only the chosen group matters
    • A permutation: the form gives each book a different role
    • The sum rule: each selected book is a separate outcome

  4. Mei and Sol are selected for first and second speaking slots. This is a combination because the speakers were selected.

    Circle one:   True   False

  5. Arrange all the letters of LEVEL, with V required to be first. Copies of the same letter are identical. How many distinct rows are possible?

    • 12
    • 30
    • 24
    • 6

  6. How many distinct arrangements do the letters of LEVEL have?

    • 30
    • 120
    • 60

  7. How many 2-person teams can form from 7 players? Type the number.

    Answer: ______________

  8. A group chooses 7 of its 9 members for a committee with equal duties. Count by choosing the members left out. How many committees are possible?

    Answer: ______________

  9. Ben counts 4-person committees from 9 people as (9 × 8 × 7 × 6) / 4 = 756. What correction is needed?

    • Divide by 4 as Ben did; four members give four listings
    • Divide by 24; each committee has 24 listings, giving 126
    • Divide by 6; swapping a pair removes all repeats, giving 504

  10. Use all the letters in BANANA in a row. Copies of the same letter are identical. How many distinct rows are possible?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Order matters, or it does not W1-mt_1L58kuu-w3-s1

  1. 20 · Gold and silver are distinct roles. There are 5 gold winners to choose from, then 4 silver winners, giving 20 outcomes.
  2. 4 · Fix A, then choose its partner from B, C, D and E. These four partners give four loans.
  3. A combination: only the chosen group matters · The outcome is the group of borrowed books. Listing that group in another order does not create a new loan.
  4. False · The word 'selected' does not settle the count. First and second are distinct slots, so switching speakers changes the schedule.
  5. 6 · Fix V, then arrange two Ls and two Es. The count is 4! / (2! × 2!) = 6.
  6. 30 · LEVEL repeats E and L, so divide 120 by 2 factorial twice: 30.
  7. 21 · Choosing 2 from 7 is 7 times 6 divided by 2, which is 21.
  8. 36 · Each committee leaves out two members, and each excluded pair determines one committee. C(9,2) = 36.
  9. Divide by 24; each committee has 24 listings, giving 126 · Four distinct members have 4! = 24 ordered listings. The ordered count is 3024, so 3024 / 24 = 126 committees.
  10. 60 · There are three As, two Ns and one B. Divide 6! by 3! × 2!: 720 / 12 = 60.
Worksheet · LightMySky