Probability using permutations and combinations

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   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?

   5/42
2. 2.

   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?

   3/28
3. 3.

   Tala draws 3 of 9 topping slips from a bag at random, without putting any back; 6 are vegetables and 3 are fruits. What is the chance all 3 are vegetables, in simplest form?

   5/21
4. 4.

   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?

   5/11
5. 5.

   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?

   7/22
6. 6.

   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?

   15/56
7. 7.

   Jun's teacher picks 4 of 9 songs at random from 5 fast and 4 slow songs. What is the chance exactly 2 are fast, in simplest form?

   10/21
8. 8.

   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?

   1/42
9. 9.

   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?

   1/35
10. 10.

    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?

    1/36