A person going to a party was asked to bring 2 different bags of chips. Going to the store, she finds 15 varieties. How many different selections can she make?

Answer 1

Let's say that among the chips on the shelf are Nacho Cheese Doritos and Cool Ranch Doritos. Can you see that if the person picks Nacho Cheese first and then Cool Ranch that the result is the same as if they picked Cool Ranch first and then Nacho Cheese? Either way they have a pick that consists of one pack of each. This means that this problem is about combinations and NOT permutations.

The equation for combinations is:

where "n" is the total number to pick from (in this case 15) and "r" is the number you are picking (in this case 2)

So:

Answer 2

Hi Emily,

Order of chip selection does not matter, so this is a combination problem. Formula for that is:

C(n,x)=n!/x!(n-x)!

Breaking this down:

C implies combination, not a variable

n=total sample size, number of chip varieties available in this case

x=number selected

!=factorial, n*(n-1)*(n-2) etc. Ex. 3*2*1=3!=3 factorial

Now, let's identify these variables for our problem:

n=15

x=2

So:

C(15,2)=15!/(2!*13!)

You can input "factorial" into most graphics calculators (TI-83 series, etc.), but let me know if you require hand calculation. Anyway:

C(15,2)=105

105 possible combinations of chips. I hope this helps.