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Grade 11 · Math · Algebra 2

11th grade Permutations and combinations worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Permutations and combinations

Grade 11 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

  1. Read this first

    Outcome list, started

    A in front: AB, AC, AD, AE, AF, AG. B in front: BA, BC, BD, BE, BF, BG. The list goes on the same way with C to G in front.

  2. Kira chooses who sits in the front seat and who sits in the back seat of a two-seat boat from 7 friends, A to G. How many seatings are possible?

  3. Tree, started

    6 branches for the left seat. Under A: 5 branches for the middle seat (B, C, D, E, F). Under A then B: 4 branches for the right seat (C, D, E, F).

  4. Luz fills the left, middle and right seats of the front row from 6 friends, A to F, one friend per seat. How many seatings are possible?

  5. Ordered list

    5 × 4 × 3 rows. The set A, B, C shows up as 3 × 2 × 1 rows: ABC, ACB, BAC, BCA, CAB, CBA.

  6. Pia chooses 3 of 5 library books, A to E, to take home. How many different sets of 3 books are possible?

  7. Ordered list

    6 × 5 × 4 × 3 rows. Each group of 4, like ABCD, shows up as 4 × 3 × 2 × 1 rows.

  8. Ren picks 4 of 6 friends, A to F, to share a tent. How many different groups of 4 are possible?

  9. Tala sets 6 different plants in a row on the windowsill. How many different orders are possible?

  10. Zee stacks 4 different books in one pile on a desk. How many different orders are possible?

  11. Bo sets the running order for 7 friends in a relay, one runner for each leg. How many running orders are possible?

  12. Esme checks a homework answer for P(9, 2), the number of ordered pairs from 9 things. What is P(9, 2)?

  13. Jun works out P(10, 2), the number of ordered pairs from 10 things, for math club. What is P(10, 2)?

  14. Kira checks a homework answer for C(8, 3), the number of groups of 3 from 8 things. What is C(8, 3)?

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11th grade Permutations and combinations worksheet – printable
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About this worksheet

Permutations and combinations. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can count ordered rows with the product rule, and write the count as P(n, r) or n!.
  • I can cross out the reorderings to count groups, C(n, r) = P(n, r) ÷ r!, and tell which one a story needs.
  • I can count two groups chosen together, or a special job plus a group, and check big counts on a calculator.

Standard: S-CP.B.9 (+)

Words to know

outcome list: Every possible result written as one row; a tree draws the same rows as paths.

product rule: Multiply the choices for each pick to count the rows.

permutation: An ordered arrangement; P(n, r) counts r picks from n, in order.

combination: A group with no order; C(n, r) counts groups of r from n.

factorial: n! = n × (n − 1) × … × 1, every order of n things.

reordering: The same group written in a different order: AB and BA.

Common mistakes

Counted every order of a group as a new group, so a team or a set of toppings was counted several times. List the pairs from A, B, C together and cross out BA, CA and CB.

Crossed out orders that are really different, such as a president and a treasurer swapping jobs.

Lined up everyone when only a few places were filled. Ask how many places there are, and stop multiplying after that many.

What to say

Ask: if two people swap places, is it a new way?

Questions parents ask

What is the most common mistake with permutations and combinations?

Counted every order of a group as a new group, so a team or a set of toppings was counted several times. List the pairs from A, B, C together and cross out BA, CA and CB.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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