math project matrix
TRANSCRIPT
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A soccer club has 22 players, including C.Ronaldo and
Fredinand.
Ronaldo Ferdinand
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One day, the coach has to choose 12 players from 22 players to participate in the league.
Whoa! We MUST win this little thing !!!
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What’s the probability that :
Ronaldo and Ferdinand are both chosen for the team ?
You two come here !Quick !
What ???
YAY !!!
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In this problem, the coach has to choose 12 players amongst 22 players.
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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.)
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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.
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In this problem, the coach has to choose 12 players amongst 22 players.
FIRST STEP...
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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
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The number of ways to choose 12 player from 22 players is presented by this equation :
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The number of ways to choose 12 player from 22 players is presented by this equation :
C
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22
The number of ways to choose 12 player from 22 players is presented by this equation :
C
22 players of the club
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12
The number of ways to choose 12 player from 22 players is presented by this equation :
22C
Choose 12 players from 22 players
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The number of ways to choose 12 player from 22 players is presented by this equation :
22C12 =
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The number of ways to choose 12 player from 22 players is presented by this equation :
22C12 = 646646
Ok now we got this : 646646
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In this problem, the coach has to choose 12 players amongst 22 players.
SECOND STEP...
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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
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The number of ways to choose both Ronaldo and Ferdinand is presented by this equation:
C
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22
The number of ways to choose both Ronaldo and Ferdinand is represented by this equation:
C
This number represents 2 players (Ronaldo and Ferdinand)
Choose 2 players (both Ronaldo and Ferdinand)
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20
The number of ways to choose both Ronaldo and Ferdinand is represented by this equation:
2C2 . C
The remaining of the team ( after both Ronaldo and Ferdinand are chosen.)
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10
The number of ways to choose both Ronaldo and Ferdinand is presented by this equation:
2C2 . 20C
Choose another 10 players from the remaining of the team
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Now we got this second number : 184756 ways
The number of ways to choose both Ronaldo and Ferdinand is presented by this equation:
2C2 . 20C10 =184756
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The probability that both Ronaldo and Ferdinand are chosen is represented by this equation :
2C2 . 20C10
Number of ways to choose both Ronaldo and Ferdinand
P =
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The probability that both Ronaldo and Ferdinand are chosen is represented by this equation :
2C2 . 20C10
22C12
Number of ways to choose 12 players from 22 players
P =
=
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The probability that both Ronaldo and Ferdinand are chosen is represented by this equation :
2C2 . 20C10
22C12 P =
=28.57%
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The team goes to final and wins the Cup.
We won ?Ooh, I’m not surprised.
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To celebrate, the coach decides to buy a new car …
Nissan ?Acura ?Dodge ?
Chevrolet ?
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Finally, the coach decided to buy the 2009 Lamborghini Gallardo
Perfect !!!
<3 <3 this …
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The price of the car is $ 200,000 (taxes added already.)
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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
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The bank charges 7% interest compound monthly and the loan must be repaid in 3 years !!
I% = 7
N = 3 years
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Question :
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Question :
Calculate the monthly payment of the team if they decide to loan.
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Open your calculator and launch the TVM Solver program. Then enter the value in next slide:
TVM Solver
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Step by Step
N = 36 (3 years = 36 months)
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Step by Step
N = 36I% = 7 (The interest rate is 7% )
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Step by Step
N = 36I% = 7PV = $200,000 – $150,000
= $50,000
The prize money
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Step by Step
N = 36I% = 7PV = $ 50,000
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Step by Step
N = 36I% = 7PV = $ 50,000FV = 0 (the loan will be repaid after 3 years)
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Step by Step
N = 36I% = 7PV = $ 50,000FV = 0 P/Y = 12 (pay monthly)
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Step by Step
N = 36I% = 7PV = $ 50,000FV = 0 P/Y = 12 C/Y = 12 (compound monthly)
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Step by Step
N = 36I% = 7PV = $ 50,000FV = 0 P/Y = 12 C/Y = 12
And move the cursor to the PMT and press [alpha] [enter] to solve for the monthly payment.
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Step by Step
N = 36I% = 7PV = $ 50,000FV = 0 P/Y = 12 C/Y = 12 PMT = - $1543.85
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$ 1543.85
Conclusion
The monthly payment that the club would pay if they decided to take the loan is :