ANSWERS

PERMUTATIONS AND COMBINATIONS WORKSHEET

1. a) 6 · 5 = 30 b) 6 · 6 = 36

2. 5 · 4 = 20

3. a) 4 · 5 · 2 = 40 b) 5 · 6 · 3 = 90

4. 5^15 = 30,517,578,125

5. a) 6! = 720  b) C(6, 2) · C(4, 2) = 90  c) C(6, 3) = 20 d) C(6, 3) · C(3, 2) = 60

6. P(5, 5) = 5! = 120

7. 5! − 4 · 2 · 3! = 72

8. 8!/8 = 7! = 5040

9. 5! = 120

10. 5!/2!= 60

11. 10!/(3!3!2!)= 50, 400

12. 8!/(3!2!) = 3360

13. C(10, 5) · C(5, 4) = 1260

14. C(8, 3) · C(5, 4) = 280

15. a) 2^20 = 1, 048, 576 b) C(20, 7) = 77, 520 c) C(20, 10) = 184, 756

16. a) C(7, 2) = 21 b) C(4, 2) = 6 c) C(4, 1) · C(3, 1) = 12

17. C(4, 2) · C(7, 3) · C(3, 1) = 630

18. C(7, 1) · C(6, 3) · C(3, 2) = 420

19. 3^10 = 59, 049

20. 5^6 = 15, 625