Combinations

Today in class, we learned about combinations. We first determined the differences between Combinations and Permutations.
Basically,
Permutations                                        Combinations 
1.) Select                                                1.) Select
2.) Arrange

There is also certain words/hints that you can look for in the question that can help you determine which method to use to solve.

For example;

with Permutations, you might find the words arranged or different. when dealing with Combinations, you might find the words select or choose.

you must use the formula when dealing with Combination - can not use the dash method. The formula will look like this: nCr =     n!       
                                  r! (n-r)!

An Example of a Combination question:
A student has a penny, a nickel, a dime, a quarter, and a half dollar and wishes to leave a tip of exactly 3 coins. How many different tips are possible?
You can tell it's a Combination question because the arrangement of the coins is not necessary. you are simply selecting the coins. 

Solution:
n = 5            
r = 3
5C3 =   5!        
            3! (5-3)!

        =   5!       
           3! 2!
     
        =   5x4x3!          - At this point,3! cancels out 3! and 2! simplifys the 4 into a 2. 
             3! 2!

       =  5x2x3!
            3! 2! 

       = 10 

IMPORTANT PROVINCIAL EXAM NOTE: 

nCx = nCy 
n = x + y