Permutations and combinations

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. Read this first

   Outcome list, started

   A in front: AB, AC, AD, AE, AF, AG. B in front: BA, BC, BD, BE, BF, BG. The list goes on the same way with C to G in front.

2. 1.

   Kira chooses who sits in the front seat and who sits in the back seat of a two-seat boat from 7 friends, A to G. How many seatings are possible?

   42

3. Tree, started

   6 branches for the left seat. Under A: 5 branches for the middle seat (B, C, D, E, F). Under A then B: 4 branches for the right seat (C, D, E, F).

4. 2.

   Luz fills the left, middle and right seats of the front row from 6 friends, A to F, one friend per seat. How many seatings are possible?

   120

5. Ordered list

   5 × 4 × 3 rows. The set A, B, C shows up as 3 × 2 × 1 rows: ABC, ACB, BAC, BCA, CAB, CBA.

6. 3.

   Pia chooses 3 of 5 library books, A to E, to take home. How many different sets of 3 books are possible?

   10

7. Ordered list

   6 × 5 × 4 × 3 rows. Each group of 4, like ABCD, shows up as 4 × 3 × 2 × 1 rows.

8. 4.

   Ren picks 4 of 6 friends, A to F, to share a tent. How many different groups of 4 are possible?

   15
9. 5.

   Tala sets 6 different plants in a row on the windowsill. How many different orders are possible?

   720
10. 6.

    Zee stacks 4 different books in one pile on a desk. How many different orders are possible?

    24
11. 7.

    Bo sets the running order for 7 friends in a relay, one runner for each leg. How many running orders are possible?

    5040
12. 8.

    Esme checks a homework answer for P(9, 2), the number of ordered pairs from 9 things. What is P(9, 2)?

    72
13. 9.

    Jun works out P(10, 2), the number of ordered pairs from 10 things, for math club. What is P(10, 2)?

    90
14. 10.

    Kira checks a homework answer for C(8, 3), the number of groups of 3 from 8 things. What is C(8, 3)?

    56