Grade 11 · Math · Algebra 2

11th grade Permutations and combinations worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Permutations and combinations

Grade 11 Math Worksheet - Challenge Me

NameDate

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

Noah's student council picks 2 of 7 seventh graders and 2 of 6 eighth graders. How many different councils of 4 are possible?
Pia picks 2 of 6 vegetable toppings and 1 of 3 cheeses for a pizza. How many different pizzas are possible?
Ren packs 3 of 7 novels and 2 of 4 comic books for a trip. How many different sets of 5 books are possible?
Zee's team of 9 picks a captain, then 3 more players from the rest for a skills show. How many ways can this be done?
Bo's class of 10 picks a leader, then a 2-person crew from the rest, to run the book swap. How many ways are possible?
Esme's group of 8 campers picks a tent leader, then 4 tent mates from the rest. How many ways are possible?
Kira's class of 25 picks a book committee of 4. Using a calculator, how many different committees are possible?
Luz's club of 20 elects a president, vice president, secretary and treasurer, one job each. Using a calculator, how many ways can the jobs be filled?
Milo picks 6 of 30 library books for a classroom box. Using a calculator, how many different boxes are possible?
Noah's race has 18 runners, and the top 5 places get ribbons. Using a calculator, how many ways can the 5 ribbons be given?

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.

More algebra 2

See all Algebra 2

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records