The document discusses a soccer club that has 22 players and needs to choose 12 players for a league. It calculates the probability that two specific players, Ronaldo and Ferdinand, will both be chosen. It then describes the soccer team winning a cup and their coach wanting to buy a expensive car. As they do not have enough money, they consider taking out a loan. It proceeds to calculate the monthly payment if they take out a 3-year loan at 7% interest to cover the remaining cost of the car.

1. Problems

2. A soccer club has 22 players, including C.Ronaldo and Fredinand. Ronaldo Ferdinand

3. One day, the coach has to choose 12 players from 22 players to participate in the league. Whoa! We MUST win this little thing !!!

4. What’s the probability that : Ronaldo and Ferdinand are both chosen for the team ? You two come here ! Quick ! What ??? YAY !!!

5. In this problem, the coach has to choose 12 players amongst 22 players .

6. In this problem, the coach has to choose 12 players amongst 22 players. So the order doesn’t matter (because we do not really care who the coach will choose first.)

7. In this problem, the coach has to choose 12 players amongst 22 players. So the order doesn’t matter (because we do not really care who the coach will choose first.) => We can use the “Choose” formula to solve this problem.

8. In this problem, the coach has to choose 12 players amongst 22 players. FIRST STEP...

9. In this problem, the coach has to choose 12 players amongst 22 players. FIRST STEP... Calculate the number of ways to choose 12 players from 22 players

10. The number of ways to choose 12 player from 22 players is presented by this equation :

11. The number of ways to choose 12 player from 22 players is presented by this equation : C

12. The number of ways to choose 12 player from 22 players is presented by this equation : 22 C 22 players of the club

13. The number of ways to choose 12 player from 22 players is presented by this equation : 22 C 12 Choose 12 players from 22 players

14. The number of ways to choose 12 player from 22 players is presented by this equation : 22 C 12 =

15. The number of ways to choose 12 player from 22 players is presented by this equation : 22 C 12 = 646646 Ok now we got this : 646646

16. In this problem, the coach has to choose 12 players amongst 22 players. SECOND STEP...

17. In this problem, the coach has to choose 12 players amongst 22 players. SECOND STEP... Calculate the number of ways to choose both Ronaldo and Ferdinand

18. The number of ways to choose both Ronaldo and Ferdinand is presented by this equation: C

19. The number of ways to choose both Ronaldo and Ferdinand is presented by this equation: 2 C 2 This number represents 2 players (Ronaldo and Ferdinand) Choose 2 players (both Ronaldo and Ferdinand)

20. The number of ways to choose both Ronaldo and Ferdinand is represented by this equation: 2 C 2 . 20 C The remaining of the team ( after both Ronaldo and Ferdinand are chosen.)

21. The number of ways to choose both Ronaldo and Ferdinand is presented by this equation: 2 C 2 . 20 C 10 Choose another 10 players from the remaining of the team

22. The number of ways to choose both Ronaldo and Ferdinand is presented by this equation: 2 C 2 . 20 C 10 = 184756 Now we got this second number : 184756 ways

23. The probability that both Ronaldo and Ferdinand are chosen is represented by this equation : 2 C 2 . 20 C 10 Number of ways to choose both Ronaldo and Ferdinand P =

24. The probability that both Ronaldo and Ferdinand are chosen is represented by this equation : 2 C 2 . 20 C 10 22 C 12 Number of ways to choose 12 players from 22 players P = =

25. The probability that both Ronaldo and Ferdinand are chosen is represented by this equation : 2 C 2 . 20 C 10 22 C 12 P = = 28.57%

26. The team goes to final and wins the Cup. We won ? Ooh, I’m not surprised.

27. To celebrate, the coach decides to buy a new car … Nissan ? Acura ? Dodge ? Chevrolet ?

28. Finally, the coach decided to buy the 2009 Lamborghini Gallardo Perfect !!! <3 <3 this …

29. The price of the car is $ 200,000 (taxes added already.)

30. The price of the car is $ 200,000 plus taxes. They had $ 150,000 as the prize for winning the Cup. They need a loan to buy that car. $ 150,000

31. The bank charges 7% interest compound monthly and the loan must be repaid in 3 years !! I% = 7 N = 3 years

32. Question :

33. Question : Calculate the monthly payment of the team if they decide to loan.

34. Open your calculator and launch the TVM Solver program. Then enter the value in next slide: TVM Solver

35. Step by Step N = 36 (3 years = 36 months)

36. Step by Step N = 36 I% = 7 (The interest rate is 7% )

37. Step by Step N = 36 I% = 7 PV = $200,000 – $150,000 = $50,000 The prize money

38. Step by Step N = 36 I% = 7 PV = $ 50,000

39. Step by Step N = 36 I% = 7 PV = $ 50,000 FV = 0 (the loan will be repaid after 3 years)

40. Step by Step N = 36 I% = 7 PV = $ 50,000 FV = 0 P/Y = 12 (pay monthly)

41. Step by Step N = 36 I% = 7 PV = $ 50,000 FV = 0 P/Y = 12 C/Y = 12 (compound monthly)

42. Step by Step N = 36 I% = 7 PV = $ 50,000 FV = 0 P/Y = 12 C/Y = 12 And move the cursor to the PMT and press [alpha] [enter] to solve for the monthly payment.

43. Step by Step N = 36 I% = 7 PV = $ 50,000 FV = 0 P/Y = 12 C/Y = 12 PMT = - $1543.85

44. Conclusion The monthly payment that the club would pay if they decided to take the loan is : $ 1543.85