Grade 11 · Math · Algebra 2

11th grade Probability using permutations and combinations worksheet

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Probability using permutations and combinations

Grade 11 Math Worksheet

NameDate

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

A committee of 3 is chosen at random from Noah's club of 5 seventh graders and 4 eighth graders. What is the chance all 3 are seventh graders, in simplest form?
Pia draws 3 of 10 letter tiles from a bag at random, without putting any back, and 4 tiles are vowels. What is the chance all 3 are consonants, in simplest form?
Ren picks 2 of 8 books at random from a shelf of 3 mysteries and 5 comics. What is the chance both are mysteries, in simplest form?
Zee picks 4 of 11 books at random from 6 novels and 5 comics. What is the chance exactly 2 are comics, in simplest form?
A team of 3 is picked at random from Bo's group of 7 sixth graders and 5 seventh graders. What is the chance exactly 1 is a sixth grader, in simplest form?
Esme draws 3 of 8 letter tiles from a bag at random, without putting any back; 3 are vowels. What is the chance exactly 2 are vowels, in simplest form?
Kira's new locker code is 4 different digits from 0 to 9, set at random. What is the chance all 4 digits are odd, in simplest form?
Luz draws 7 name slips from a hat at random, without putting any back, to set the order of 7 talks. What is the chance the 3 shortest talks come first, in any order?
Milo's bike lock code is 2 different letters from A to H, set at random. What is the chance both letters are vowels, in simplest form?
Noah's coach sets a random running order for 9 relay runners. What is the chance the 2 newest runners run first and second, in either order, 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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