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!(n−r)!r!C(n,r)=n!(n−r)!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. 6−3+8−3=86−3+8−3=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
Candela Citations
- Precalculus. Authored by: OpenStax College. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution