Probability using permutations and combinations

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   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?

   13/14
2. 2.

   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?

   17/24
3. 3.

   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?

   85/99
4. 4.

   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?

   3/10
5. 5.

   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?

   1/6
6. 6.

   Jun draws 4 of 11 topping slips from a bag at random, without putting any back. What is the chance the pepper slip is one of them, in simplest form?

   4/11
7. 7.

   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?

   8/33
8. 8.

   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?

   2/7
9. 9.

   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?

   1/4
10. 10.

    Pia's teacher picks 3 of 11 songs at random from 4 pop, 4 jazz and 3 folk songs. What is the chance of one of each kind, in simplest form?

    16/55