How many possibilities formula

For example let's say we have a password combination of a,b,c,d , if the password length was 1 then we'll have 4 possible passwords a,b,c,d , now if the length was 2 then we'll have 20 possible passwords a,b, Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?

Learn more. How to calculate the number of possibilities? Ask Question. Also referred to as r-combination or "n choose r" or the binomial coefficient. In some resources the notation uses k instead of r so you may see these referred to as k-combination or "n choose k. You have won first place in a contest and are allowed to choose 2 prizes from a table that has 6 prizes numbered 1 through 6.

How many different combinations of 2 prizes could you possibly choose? In this example, we are taking a subset of 2 prizes r from a larger set of 6 prizes n. A teacher is going to choose 3 students from her class to compete in the spelling bee. She wants to figure out how many unique teams of 3 can be created from her class of Think about the ice cream being in boxes, we could say "move past the first box, then take 3 scoops, then move along 3 more boxes to the end" and we will have 3 scoops of chocolate!

So it is like we are ordering a robot to get our ice cream, but it doesn't change anything, we still get what we want. We can write this down as arrow means move , circle means scoop.

So instead of worrying about different flavors, we have a simpler question: "how many different ways can we arrange arrows and circles? Notice that there are always 3 circles 3 scoops of ice cream and 4 arrows we need to move 4 times to go from the 1st to 5th container. In other words it is now like the pool balls question, but with slightly changed numbers. And we can write it like this:. But knowing how these formulas work is only half the battle. Figuring out how to interpret a real world situation can be quite hard.

To help you to remember, think " P ermutation P osition". Example: what order could 16 pool balls be in? After choosing, say, number "14" we can't choose it again. Examples: 4! For example, if you have just been invited to the Oscars and you have only 2 tickets for friends and family to bring with you, and you have 10 people to choose from, and it matters who is to your left and who is to your right, then there are exactly 90 possible solutions to choose from.

Permutations come a lot when you have a finite selection from a large set and when you need to arrange things in particular order, for example arranging books, trophies, etc. Calculating permutations is necessary in telecommunication and computer networks, security, statistical analysis. A given phone area prefix can only fit in that many numbers, the IPv4 space can only accommodate that many network nodes with unique public IPs, and an IBAN system can only accommodate that many unique bank accounts.

Here is a more visual example of how permutations work. Say you have to choose two out of three activities: cycling, baseball and tennis, and you need to also decide on the order in which you will perform them. The possible permutations would look like so:.

To calculate the number of possible permutations of r non-repeating elements from a set of n types of elements, the formula is:. The above equation can be said to express the number of ways for picking r unique ordered outcomes from n possibilities.