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.


So the order doesn’t matter (because we do not really care who the coach will choose first.)


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.


FIRST STEP...


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 :


C


22C22 players of the club


22C12Choose 12 players from 22 players


22C12 =


22C12 = 646646

Ok now we got this : 646646 ways


SECOND STEP...


SECOND STEP...

Calculate the number of ways to choose both Ronaldo and Fredinand

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

C


2C2This number represents 2 players (Ronaldo and Ferdinand)

Choose 2 players (both Ronaldo and Ferdinand)


2C2 . 20C

The remaining of the team ( after both Ronaldo and Ferdinand are chosen.)


2C2 . 20C10

Choose another 10 players from the remaining of the team


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 =


2C2 . 20C10

22C12

Number of ways to choose 12 players from 22 players

P = =


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 plus taxes.

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.

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

Question :

Question :

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

You will need your calculator and the TVM Solver program :

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

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 PMT = - $1543.85

Conclusion

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

% 1543.85

The passing lesson…

One day, the coach wants the team to have a training about strategy.

Today, they will have the passing training.The strategy map will be shown in the next

slide.

Goal Keeper

D1 D2 D3

M1 M2

F1

D : Defender

M : Midfielder

F : Forward

Question a

How many ways can the ball be passed from the goal keeper to F1 ?

Question a

How many ways is the least ways that the ball can be passed from the goal keeper to F1 ?

To answer this question, we have to take a look at the system again.

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 1

0 0 0 01 1

0 0 0 0 0

0 0 0 0 0 1

1

G.K

G.K

0 1 1 1 0 0 0

0 0

0

0

0

0 0 0 0 0 10

0 0 0 0 0 0 0

To find the number of ways to pass from GK to F1, we need to square the matrix. The squared matrix will represent the ways to pass after the GK pass the ball 2 times.

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 1

0 0 0 01 1

0 0 0 0 0

0 0 0 0 0 1

1

G.K

G.K

0 1 1 1 0 0 0

0 0

0

0

0

0 0 0 0 0 10

0 0 0 0 0 0 0

You will need your calculator. Go [2nd] [x-1] to go to the Matrix Menu.

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 1

0 0 0 01 1

0 0 0 0 0

0 0 0 0 0 1

1

G.K

G.K

0 1 1 1 0 0 0

0 0

0

0

0

0 0 0 0 0 10

0 0 0 0 0 0 0

You will need your calculator. Go [2nd] [x-1] to go to the Matrix Menu.

And then put the matrix to matrix [A] with the side 7x7.

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 1

0 0 0 01 1

0 0 0 0 0

0 0 0 0 0 1

1

G.K

G.K

0 1 1 1 0 0 0

0 0

0

0

0

0 0 0 0 0 10

0 0 0 0 0 0 0

Then back to the home screen, hit [2nd] [x-1] [enter] to put matrix [A] onto the home screen. Then hit [x2] and then [enter].

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 0

0 0 0 20 0

0 0 0 0 1

0 0 0 0 0 0

0

G.K

G.K

0 0 0 0 2 2 0

0 1

0

0

0

0 0 0 0 0 00

0 0 0 0 0 0 0

AND we got this one.

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 0

0 0 0 20 0

0 0 0 0 1

0 0 0 0 0 0

0

G.K

G.K

0 0 0 0 2 2 0

0 1

0

0

0

0 0 0 0 0 00

0 0 0 0 0 0 0

As we see, the GK still can’t pass the ball to F1 after 2 times pass. Because the number from GK to F1 is still 0.

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 0

0 0 0 20 0

0 0 0 0 1

0 0 0 0 0 0

0

G.K

G.K

0 0 0 0 2 2 0

0 1

0

0

0

0 0 0 0 0 00

0 0 0 0 0 0 0

Then we will take the cubic of matrix [A] and let’s see if the

GK can pass the ball to F1.

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 0

0 0 0 20 0

0 0 0 0 1

0 0 0 0 0 0

0

G.K

G.K

0 0 0 0 2 2 0

0 1

0

0

0

0 0 0 0 0 00

0 0 0 0 0 0 0

Take the matrix [A] from the matrix window and then hit [^] and then [3]. Hit [enter].

D1 D2 D3 M1 M2 F1

D1

D2

D3

M1

M2

F1

0 0 0 0 0

0 0 0 00 0

0 0 0 0 0

0 0 0 0 0 0

0

G.K

G.K

0 0 0 0 0 0 4

0 0

0

0

0

0 0 0 0 0 00

0 0 0 0 0 0 0

And we got the 3rd matrix like this. As we can see, the number from GK to F1 is now 4. It means after the GK passed 3 times, there will be 4 passes straight from GK to F1.

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Math Project Matrix