Probability using permutations and combinations

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   MO, MP, MC, MT, OP, OC, OT, PC, PT, CT. Noah draws 2 of 5 topping slips, M, O, P, C and T, from a bag at random, without putting the first back. What is the chance C (corn) is one of them?

   2/5
2. 2.

   AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF. Pia picks 2 of 6 books, A to F, at random for a trip, and A, B and C are mysteries. What is the chance both books are mysteries, in simplest form?

   1/5
3. 3.

   PL, PA, PN, PE, PT, LA, LN, LE, LT, AN, AE, AT, NE, NT, ET. Ren draws 2 of the 6 letter tiles P, L, A, N, E and T from a bag at random, without putting the first back. What is the chance neither tile is a vowel?

   2/5
4. 4.

   Tala draws all 4 name slips of a relay team from a hat at random, without putting any back, to set the running order. What is the chance the order is alphabetical, in simplest form?

   1/24
5. 5.

   Zee's new locker code is 3 different digits from 1 to 5, set at random. What is the chance a friend guesses it on the first try, in simplest form?

   1/60
6. 6.

   Bo's bike lock code is 2 different letters from A to F, in order, set at random. What is the chance one guess opens it, in simplest form?

   1/30
7. 7.

   Esme puts 5 different books on a shelf in a random order. What is the chance they end up in order of height, shortest first, in simplest form?

   1/120
8. 8.

   Jun's teacher picks 2 of 6 songs at random for the warm-up. What is the chance the 2 picks are the 2 newest songs, in simplest form?

   1/15
9. 9.

   Kira's class of 7 picks 2 students at random to water the plants. What is the chance the 2 who sit by the window are picked, in simplest form?

   1/21
10. 10.

    Milo draws 3 of 8 topping slips from a bag at random, without putting any back. What is the chance the slips are mushroom, pepper and olive, in simplest form?

    1/56