Perms and Combs, Videos attached

Permutations and combinations are often misused and interchanged comfortably, along with arrangements, collections and groupings. It’s often easy to misuse them, but there is a slight difference in their meanings:

Permutations: An arrangement of a set of events or objects, where in the order of the events MATTERS.

Example: The arrangement of the numbers 1, 2, 3 and 1, 3, 2 is a different PERMUTAION.

Combinations: An arrangement of a set of events or objects, where in the order DOES NOT MATTER.

Example (follow-up): The arrangement of the numbers 1, 2, 3 and 1, 3, 2 is THE SAME COMBINATION.

The knowledge of the difference of meaning in these concepts is crucial.

There are different mathematical formulas for calculating permutation and combination arrangements. It is very important, however, to be able to logically analyze if the order in the arrangement matters.

For permutations:

 For combinations:

The only difference between the two is that in the combination formula, it is essential to divide the result by the number of ways the objects or events can inter-arrange to switch their order, because the order is irrelevant.

The following videos provide a very helpful visual guide to help further develop an understanding of these concepts:

http://www.khanacademy.org/math/probability/v/permutations-and-combinations-1

http://www.khanacademy.org/math/probability/v/permutations-and-combinations-2

http://www.khanacademy.org/math/probability/v/permutations-and-combinations-3

http://www.khanacademy.org/math/probability/v/permutations-and-combinations-4

perms and combs

Permutations, has several different meanings, but all are related to “the act of permuting”, rearranging objects and values. They occur in almost every domain of mathematics. It is an arrangement of numbers in an order . For example there are six permutations of the set {1,2,3}, namely (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1).

The formula for permutation is:

                                nPr =n!/(n-r)

Combination- is a way of selecting several things out of a large group where the order doesn’t matter. In smaller cases you can count the number of combination. When the set gets larger you have to use difficult mathematics to find the number of combinations.

The combination formula:

              (nk)=n(n-1)…(n-k+1)/k(k-1)…1

Premutations and Combinations

Permutations- A permutation is a order of numbers where the order does matter
Combinations- A Combination is a order of numbers where the order does not matter

A combination lock is a perfect example of a Permutation as it is three order number line where the numbers have to be in the right order to open the lock.

If your combo is 23-67-9 you can only put it in as this order if you put 67-23-9 the numbers are the same but the order is not making it impossible to open your locker.

The order through which you put fruit into a smoothie is a combination
If Apples are 1
Banannas are 2
Peaches are 3
The order can go many ways
123
132
321
213
231
312

In other words a permutation is an ordered combination

The above formula is for Permutations without repitition the below fomule is for combinations without repitition.

where n is the number of things to choose from, and you choose r of them       (Order does not matter)

For things where repitition is allowed the formulas are as follows

Permutations is simply N to the exponent R where N is the number of things to choose from and R is how many you will choose

Combinations where repitition is allowed is shown as the formula below

where n is the number of things to choose from, and you choose r of them
(Repetition allowed, order doesn't matter)

All information was taken from the link below the above descriptions and formulas are a short sumamry of the site the site as well provides real world examples

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Combinations & Permutations.

Combinations are easy going. Order doesn’t matter. You can mix it up and it looks the same. Let’s say I’m a cheapskate and can’t afford separate Gold, Silver and Bronze medals. In fact, I can only afford empty tin cans.
How many ways can I give 3 tin cans to 8 people?
Well, in this case, the order we pick people doesn’t matter. If I give a can to Alice, Bob and then Charlie, it’s the same as giving to Charlie, Alice and then Bob. Either way, they’re going to be equally disappointed.
This raises an interesting point — we’ve got some redundancies here. Alice Bob Charlie = Charlie Bob Alice. For a moment, let’s just figure out how many ways we can rearrange 3 people.
Well, we have 3 choices for the first person, 2 for the second, and only 1 for the last. So we have 3 * 2 * 1 ways to re-arrange 3 people.
Wait a minute… this is looking a bit like a permutation! You tricked me!
Indeed I did. If you have N people and you want to know how many arrangements there are for all of them, it’s just N factorial or N!
So, if we have 3 tin cans to give away, there are 3! or 6 variations for every choice we pick. If we want to figure out how many combinations we have, we just create all the permutations and divide by all the redundancies. In our case, we get 336 permutations (from above), and we divide by the 6 redundancies for each permutation and get 336/6 = 56.
The general formula is

which means “Find all the ways to pick k people from n, and divide by the k! variants”. Writing this out, we get our combination formula, or the number of ways to combine k items from a set of n:

http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html

Enjoy!

Permutations

Permutations - An arrangement of 'n' (number) objects taking all or some of the objects at a time where the order does matter.

Without Repetition:

            Formula:  nPr = n!/(n-r)!

n - The total number of items to choose from.
r - The number of items being chosen.

ex. a) How many ways can you order billiard balls numbered 1 to 16?
 b) How many ways can you order 5 different balls?


a)
An easy way to do it is insert [1],[6],[MATH], go over to the 'Probability' option and select option 4 so it will look like this on your calculator:

16!

Really all '!' is, is a short cut for going 16x15x14x13x12xx11x10x9x8x7x6x5x4x3x2x1
answer: 20922789888000 or 2.09x10¹³

b)
 You can use the formula nPr = n!/(n-r)! 
n=16
r=5                     =16!/(16-5)!
                           =16!/11!
                           =524160
or with your calculator you can take a shortcut by inserting "16" then [MATH] button, over to probability and select option 2 "nPr"than insert the number "5". It should look like this on your calculator.

16 nPr 5

Hit solve and you should get the same answer as above: "524160".

BUYING AND LEASING A CAR TERMS


BUYING:TO EXCHANGE MONEY FOR ITS EQUIVALENT


LEASING: A CONTRACT AGREEMENT TO USE A CAR OVER A PERIOD OF TIME , AND MAKING PAYMENT WHILE USING THE CAR.




        BUY AND LEASING A CAR


    PRO'S OF BUYING A CAR:


   IN THE END YOU OWN THE CAR
   YOU CAN DO AS MANY MODIFICATIONS AS YOU WANT
    YOU CAN PUT AS MY KILOMETERS ON THE CAR AS YOU LIKE


     
      CON'S OF BUYING A CAR:
ITS EXPENSIVE
YOU HAVE TO PAY FOR ALL THE REPAIRS

    PRO'S TO LEASING A CAR:
NOT AS EXPENSIVE AS BUYING A CAR
YOU DON'T HAVE TO PAY FOR REPAIRS ON THE CAR
YOU GET A NEW CAR EVERY 3 YEARS    CON'S TO LEASING A CAR:
YOU DON'T OWN THE CAR IN THE END
YOU CAN'T MODIFY THE CAR
YOU HAVE LIMITED KILOMETERS YOU CAN PUT ON THE CAR
YOU CAN'T HAVE ANY DENTS OR SCRAPES IN THE CAR WHEN YOU BRING IT BACK TO THE DEALER]

Probability – The chance or likelihood that something will happen.

Probabilities must be between 0 and 1

·         A probability of 0 means it’s impossible

·         A probability of 1 means it will definitely happen

Probabilities can be expressed as…

·         Ratio

·         Fraction

·         Decimal

·         Percent

Outcome – The result of an experiment

Sample Space – All the possible outcomes of an experiment

Event – One or more outcomes of an experiment

Type of Events

1.      Independent Event – Events that is not affected by any other events.

Ex.  A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die?

        P(head) = ½

        P(3) = 1/6

        P(head and 3) = P(head) x P(3)

                                    = (1/2) X (1/6)

                                 = 1/12

2.      Dependent Event – Events that can be affected by previous events.

Ex. A chosen is chosen at random from a standard deck of 52 cards. Without replacing it, a second card is chosen. What is the probability that the first chosen card chosen is a queen and the second card is a jack?

       P(queen on first pick) = 4/52

       P(jack on 2^nd pick given queen on 1^st pick) = 4/51

       P(queen and jack) = (4/52) x (4/51)

                                      = 16/2652

                                      = 4/633

3.      Simple Event – A single outcome in the sample space

Ex. What is the probability of rolling a 5?

        P(5) = 1/6

4.      Compound Events – More than one outcome in the sample space

Ex. What is the probability of rolling an even number?

       Ex. P(even) = 3/6

                           = 1/2

Factorial – The result of multiplying a series of decreasing numbers

Note: The factorial for 0 is always 1

Ex. 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362 880

Ex. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Probability

Probability = (desired outcome)                   Ex.   P(heads)= 1/2 = 50% = .5
                   ( total # of outcomes)


The types of probability:
1. Theoretical- what the results should look like in theory.
 Ex. flipping a coin and getting heads is 1/2 or 50%


2. Experimental- The results are found out in tests.
Ex. flipping a coin 100 times and getting heads 56 times


This type of probability isn't accurate if very few trials are done.


Tree diagrams:
The outcomes for 2 probabilities; flipping a coin and rolling a die.


or it can be written in a table called a sample space


Sample space
H-1       T-1
H-2       T-2
H-3       T-3
H-4       T-4
H-5       T-5
H-6       H-6

To find the probability of 2 events occurring at the same time you multiply both the probabilities together.


Ex. Probability of getting heads is 1/2 and rolling a 5 is 1/6 so 1/2 x 1/6 = 1/12 

Using TVM solver

N: Total # of payments to the account.
I%: Annual interest rate as a '%'.
PV: Present value of the account.
PMT: Payments made to the account.
FV: Future value of the account.
P/Y: # of payments made per year.
C/Y:  # of compounded periods per year.
PMT: Depends when payments are made.

Net Worth

Net Worth ( synonymous with equity ) - the difference between the value assets(what you own) and liabilities(what you owe).

Net worth can be a useful tool to measure your financial progress from year to year.

Three categories of Assets:

a) Liquid assets (sometimes called Current Assets) - assets that can be converted into cash quickly and without financial penalty. Cash accounts, treasury bills, money market funds, Canada Savings Bonds are all invested vehicles found in this category.

b) Semi-liquid Asset - include longer term investments that are intended to sore up value for major future needs such  as education costs or retirement. It may take a while to convert it to cash and may pay fee. Some examples are: stocks, bonds, mutual funds, real estate ( other than your principal residence ), RRSPs and registered pension plans (RPPs).

c) Non-Liquid Assets - are items you acquire for your family's long term use or enjoyment. May include you home, vacation property, cars bouts, antiques, and furnishinhs.

Two types of Liabilities:

a) Short-term Debt - are all debts that must be paid within the next twelve months. Credit card balances, personal, installment and consumer loans fall into this category.

b) Long term Debt - are used for two purposes: to finance long-term investments such as real estate or the purchase of a major personal assets like you residence, vacation property or long term car loans.

Debt-equity ratio:

-Debt includes all debt ( short term or long term ) except the mortgage on you principal residence.

-DER should not exceed 50% of net worth.

                           Debt Equity Ratio (DER) = Liabilities - Mortgage

                                                                            Net Worth

more info:

http://financialplan.about.com/od/personalfinance/ht/networthhowto.htm

http://www.msmoney.com/mm/financial_health/where_stand/yournetworth.htm