Combinations

Howdy y'all! I'm Carl Manuel and I'm here to talk about COMBINATIONS!

A combination is an unordered collection of elements, unlike permutations where it is a collection of ordered elements. With a permutation, we select and order the elements (two actions). But with a combination, we only select the elements (one action). Must use the formula for a combination -- cannot use the dash method.

NOTE: In permutation, you have to select AND arrange but in combination you just have to select, no arrangement.

Example:

Permutation question

How many ways can 5 books be arranged on a shelf?

• Notice the word "arranged". Remember that combinations do not need to be arranged, hence making this question a permutation question.

Combination question

How many ways can you select two books to read on your holiday if there are 5 books to choose from?

• Words like select and choose are found in this question but it does not say to arrange so this question must be a combination question.

Formula for Combination 
*must use all the time, no dash method*

Example question:

A student has a penny, a nickel, a dime, a quarter, and a half doller and wishes to leave a tip consisting of exactly 3 coins. How many different tips are possible?

n = 5                   5 C 3    =        5!       =      5!     =    5 x 4 x 3!     =    5 x 2    =  10

r = 3                                     3! (5 - 3)!       3! 2!             3! 2! 

NOTE: N C X   =   N  C  Y           Mr. Piatek likes to put booby traps, keep that in mind. 

                        N   =   X  +  Y                                You've been warned.

RECAP:

• Combinations is an unordered collection of elements
• MUST always use formula, cannot use dash method ever.
• Combinations are only selections, no arrangements like permutations.
• If nCx = nCy , you can add x and y together to find n. ( n = x + y )
• Always read the question thoroughly. Read it once and then read it one more time. Determine whether it is permutation or combination first and then find out what the question is looking for.

Good luck everyone! Remember, if we all ace our quizzes... donuts.

Here's a picture of donuts to get you motivated!!!

Permutations With Repetition and Restrictions

Hey guys, its me Gagandeep Malhans. Today Mr. Piatek taught us some examples on Permutations with Restrictions and Repetitions.

Let's look at some examples here as follows:

Example 1: Consider the word CALCULUS.

How many distinguishable permutations can be made from the letters in CALCULUS?

We can arrange C in 2! ways, the L in 2! ways and the U in 2! way.

 (8!,2!2!2!) = 7! = 5040 ways

Example 2: Consider the five digits:  31232

How many different numbers can be formed using these digits?

We can arrange 3 in 2! ways and the 2 in 2! ways.

 (5!,2!2!) = 30 different numbers 

Here is a video of permutations with repetition and restrictions

http://www.youtube.com/watch?v=0crbJNFoMII

I hope you gain something!   :)

Hey guys, It's me Brian Laderas..

Here is an example of permutations..

1.    Compute:  5 P 5         5 · 4 · 3 · 2 · 1  =  120 2.    Compute:   6 P 2       6 · 5  =  30                or                                          multiply by two factors                                    of the factorial, starting with 6 3.    Find the number of ways to arrange 5 objects that are chosen from a set of 7 different objects.         7 P 5 =   7·6·5·4·3  =  2520      or              4.  What is the total number of possible 5-letter arrangements of the letters  w, h, i, t, e,  if each letter is used only once in each arrangement?             5 P5   =   5·4·3·2·1   =   120     or           or    simply  5!          5.   How many different 3-digit numerals can be made from the digits  4, 5, 6, 7, 8   if a digit can appear just once in a numeral?         5 P3  =   5·4·3  =  60            or

If you want to learn more, about Permutations. Just click the link down here.. If you can't click this link, just copy & paste it. http://www.youtube.com/watch?v=IGNO5ucy6eY

Hey guys, Its me Amandeep kaur  for those who don't know I sit right next to gagan and sargam.


What is factorial notation???
                     :-    For a sequence of numbers from 1 to n, where the sequence is defined by 1 * 2 * 3 * ⋅⋅⋅ * (n−2) * (n−1) * n, the notation is represented by n!. The exclamation mark is read as 'factorial'.

For example

Here is an example of factorial notation......

Solution:-

Here is a video of factorial notation

http://www.youtube.com/watch?v=pIxbYJy6YWA&safe=active


 I hope you guys learn something :)

Hello everyone I am Nabjot Brar. Today I was sitting right infront of the door beside shubham . In our first class Mr Piatek give all us a view of his lifestyle i.e what he is good at besides math , is photography  ; what all he do in vacations , his dog . It was a fun class . In this class he also showed us the binders that we have to study before precal exam .

In the second period we started unit 1 . Mr Piatek showed us the method to do permutations such as
If there are 52 runners entered in a race, in how many ways can first and second place be awarded ?
Answer
              All of them can be on the first place   = 52
              Runnersgoing to be on the 2nd place = 51
            Therefore  51×52= 2652
And Many more examples . At the end of the class we also started find the errors .
For homework he gave us fundamental counting principle worksheet.

Sorry everyone if I troubled you with my bad vocabulary . I will try to be better next time .
THANK YOU .