Solutions

Solutions to Try Its

1. 7

2. There are 60 possible breakfast specials.

3. 120

4. 60

5. 12

6. P(7,7)=5,040P(7,7)=5,040

7. P(7,5)=2,520P(7,5)=2,520

8. C(10,3)=120C(10,3)=120

9. 64 sundaes

10. 840

Solutions of Odd-Numbered Exercises

1. There are m+nm+n ways for either event AA or event BB to occur.

3. The addition principle is applied when determining the total possible of outcomes of either event occurring. The multiplication principle is applied when determining the total possible outcomes of both events occurring. The word “or” usually implies an addition problem. The word “and” usually implies a multiplication problem.

5. A combination; C(n,r)=n!(nr)!r!C(n,r)=n!(nr)!r!

7. 4+2=64+2=6

9. 5+4+7=165+4+7=16

11. 2×6=122×6=12

13. 103=1000103=1000

15. P(5,2)=20P(5,2)=20

17. P(3,3)=6P(3,3)=6

19. P(11,5)=55,440P(11,5)=55,440

21. C(12,4)=495C(12,4)=495

23. C(7,6)=7C(7,6)=7

25. 210=1024210=1024

27. 212=4096212=4096

29. 29=51229=512

31. 8!3!=67208!3!=6720

33. 12!3!2!3!4!12!3!2!3!4!

35. 9

37. Yes, for the trivial cases r=0r=0 and r=1r=1. If r=0r=0, then C(n,r)=P(n,r)=1.C(n,r)=P(n,r)=1. If r=1r=1, then r=1r=1, C(n,r)=P(n,r)=nC(n,r)=P(n,r)=n.

39. 6!2!×4!=86406!2!×4!=8640

41. 63+83=863+83=8

43. 4×2×5=404×2×5=40

45. 4×12×3=1444×12×3=144

47. P(15,9)=1,816,214,400P(15,9)=1,816,214,400

49. C(10,3)×C(6,5)×C(5,2)=7,200C(10,3)×C(6,5)×C(5,2)=7,200

51. 211=2048211=2048

53. 20!6!6!8!=116,396,28020!6!6!8!=116,396,280