DO YOU WANT TO BUILD YOUR IQ? (Combinations)

COMBINATIONS

Hello, my name is Lloyd, and I will be teaching you about Combinations.

There is a difference between Combinations and Permutations.

Permutation is when we select and order the elements.
FORMULA: nPr = n!(n-r)!


and a...


Combination is when the order does not matter and you can choose.

FORMULA: nCr = r!(n-r)! 

The n is the total and r is how many you are choosing.

YOU CANNOT USE THE DASH METHOD, USE FORMULA!

An example of a combination:

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

In this question there are 5 coins to choose from, and the student needs to pick 3 out of the 5 so you have...

n = 5 

and

 r = 3
So if you plug this in the formula you will get:

5C3 = 5! / 3!(5-3)!
     
        = 5x4x3! / 3!2!

        = 20 / 2

        = 10

There is 10 different possible combinations to tip with and the order doesn't matter.

The words I remember Mr. Piatek telling us about how to find if it's a combination is SELECT and COMMITTEE. hehe.

Also note that if the n's are the same...

nCx = nCy
n=x + y

Example: Solve for x.
xC6 = xC9
x=6+9
x=15



And thats it! Hope this helped... kind of.

I CHOOSE #18 FOR THE NEXT PERSON TO BLOG. (MARC)