Math Project Matrix

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

Ronaldo Ferdinand

One day, the coach has to choose 12 players from 22 players to participate in the league.

Whoa! We MUST win this little thing !!!

What’s the probability that :

Ronaldo and Ferdinand are both chosen for the team ?

You two come here !Quick !

What ???

YAY !!!

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

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.)

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.

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

FIRST STEP...

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

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

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

C

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

22C22 players of the club

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

22C12Choose 12 players from 22 players

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

22C12 =

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

22C12 = 646646Ok now we got this : 646646

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

SECOND STEP...

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

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

C

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

2C2This number represents 2 players (Ronaldo and Ferdinand)

Choose 2 players (both Ronaldo and Ferdinand)

The number of ways to choose both Ronaldo and Ferdinand is represented by this equation:

2C2 . 20CThe remaining of the team ( after both Ronaldo and Ferdinand are chosen.)

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

2C2 . 20C10

Choose another 10 players from the remaining of the team

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

2C2 . 20C10 =184756

Now we got this second number : 184756 ways

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 =

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 = =

The probability that both Ronaldo and Ferdinand are chosen is represented by this equation :

2C2 . 20C10

22C12 P = = 28.57%

The team goes to final and wins the Cup.

We won ?Ooh, I’m not surprised.

To celebrate, the coach decides to buy a new car …

Nissan ?Acura ?Dodge ?

Chevrolet ?

Finally, the coach decided to buy the 2009 Lamborghini Gallardo

Perfect !!!

<3 <3 this …

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

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

The bank charges 7% interest compound monthly and the loan must be repaid in 3 years !!

I% = 7

N = 3 years

Question :

Question :

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

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

TVM Solver

Step by Step

N = 36 (3 years = 36 months)

Step by Step

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

Step by Step

N = 36I% = 7PV = $200,000 – $150,000

= $50,000

The prize money

Step by Step

N = 36I% = 7PV = $ 50,000

Step by Step

N = 36I% = 7PV = $ 50,000FV = 0 (the loan will be repaid after 3

years)

Step by Step

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

Step by Step

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

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.

Step by Step

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

Conclusion

The monthly payment that the club would pay if they decided to take the loan is :

$ 1543.85