Grade 11 · Math · Algebra 2

11th grade Permutations and combinations worksheet

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Permutations and combinations

Grade 11 Math Worksheet

NameDate

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

Milo's club of 10 elects a president, a vice president and a treasurer, and no member holds two jobs. How many ways can the 3 jobs be filled?
Noah plans a set list of 4 songs, in order, from the band's 8 songs. How many different set lists are possible?
Pia seats 4 of 11 students in the 4 front-row seats of the bus, one per seat. How many seatings are possible?
Ren's locker code uses 4 different digits from 1 to 7, and the order of the digits matters. How many codes are possible?
Tala chooses 3 of 9 pizza toppings for one pizza. How many different choices of 3 toppings are possible?
Esme's class picks 3 of 10 students to plant the garden bed together. How many different groups of 3 are possible?
7.
Jun's class of 8 picks 3 students for a cleanup crew, and all 3 do the same job. Which expression counts the possible crews?
- P(8, 3)
- 8³
- C(8, 3)
- 8!
8.
Kira's class of 7 picks a line leader, a door holder and a messenger. Which expression counts the ways to fill the 3 jobs?
- C(7, 3)
- P(7, 3)
- 7!
- 7³
9.
Luz makes a playlist of 5 of 12 songs, played in a set order. Which expression counts the possible playlists?
- C(12, 5)
- 12⁵
- 12!
- P(12, 5)
10.
Milo picks 5 of 12 books to put in a reading box. Which expression counts the possible boxes?
- 12!
- P(12, 5)
- C(12, 5)
- 12⁵

11th grade Permutations and combinations worksheet – printable — Print: 1 2 3 4 5 6

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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