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

   S first: ST, SU, SV, SW, SX, SY, SZ. T first: TS, TU, TV, TW, TX, TY, TZ. The list goes on the same way for U to Z first.

2. 1.

   Jun picks a first song and a second song for the class show from 8 songs, S to Z. How many ordered pairs of songs are possible?

   56

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. 3.

   MO, MP, MT, OM, OP, OT, PM, PO, PT, TM, TO, TP. MO and OM are the same pizza. Noah picks 2 of 4 pizza toppings: mushroom (M), olive (O), pepper (P) and tomato (T). How many different pairs of toppings are possible?

   6

6. Ordered list

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

7. 4.

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

   10
8. 5.

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

   720
9. 6.

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

   24
10. 7.

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

    5040
11. 8.

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

    72
12. 9.

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

    56
13. 10.

    Luz works out C(6, 3), the number of groups of 3 from 6 things, for math club. What is C(6, 3)?

    20