Grade 11 · Math · Algebra 2

11th grade Probability using permutations and combinations worksheet

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Level: Building Confidence · On Level · Challenge Me

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Probability using permutations and combinations

Grade 11 Math Worksheet - Challenge Me

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

A committee of 4 is chosen at random from Pia's club of 6 seventh graders and 4 eighth graders. What is the chance at least one is an eighth grader, in simplest form?
Ren draws 3 of 10 letter tiles from a bag at random, without putting any back, and 3 tiles are vowels. What is the chance at least one is a vowel, in simplest form?
Tala picks 3 of 12 books at random from 5 comics and 7 novels. What is the chance at least one is a comic, in simplest form?
Zee's teacher picks 4 of 12 songs at random, and 4 of the songs are new. What is the chance at least one new song is picked, in simplest form?
A committee of 3 is picked at random from Bo's club of 10. What is the chance the club's newest member is on it, in simplest form?
Esme draws 4 of 9 letter tiles from a bag at random, without putting any back. What is the chance tiles Q and Z are both drawn, in simplest form?
Kira's teacher picks 5 of 12 books at random for a class box. What is the chance both of Kira's favorite books are in it, in simplest form?
A committee of 3 is chosen at random from 4 sixth, 2 seventh and 5 eighth graders in Luz's club. What is the chance it has one from each grade, in simplest form?
Milo draws 3 of 9 tiles from a bag at random, without putting any back: 2 are red, 4 blue and 3 green. What is the chance of one of each color, in simplest form?
Noah picks 3 of 10 books at random from 5 mysteries, 2 poetry books and 3 comics. What is the chance of one of each kind, in simplest form?

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

I can find a chance as the rows that count ÷ all the rows, counting both with order or both without.
I can use C(n, r) for committees and groups, and P(n, r) for codes and lineups.
I can find "exactly", "at least one" and "one of each" chances with counts.

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

equally likely: Every row of the list has the same chance.

at random: Picked so that every outcome is equally likely.

complement: Everything that is not the event; its chance is 1 minus the chance.

at least one: One or more; easiest as 1 minus the chance of none.

without putting back: A picked thing stays out, so the list shrinks.

Counted the bottom of the chance with order but the top without it.

Found the chance that the event does not happen. Read the question again together and circle the outcomes it asks for.

Divided by the outcomes that don't count instead of by all outcomes.

Ask: does AB count as a different outcome from BA here? Then count both the same way.

Ask: how many outcomes are there in all?

What is the most common mistake with probability using permutations and combinations?

Counted the bottom of the chance with order but the top without it.

How can I help my child with probability using permutations and combinations?

Ask: does AB count as a different outcome from BA here? Then count both the same way.

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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