When you draw five numbers out of 69 without repetition, there are 11,238,513 combinations. Let’s enter these numbers into the equation: 69 C 5 11,238,513. The above means that there are 120 ways that we could select the 5 marbles where order matters and where repetition is not allowed. For the denominator, you need to calculate 69 C 5, which equals the number of combinations when you draw five numbers from a total of 69 numbers. Refer to the factorials page for a refresher on factorials if necessary. Where n is the number of objects in the set, in this case 5 marbles. If we were selecting all 5 marbles, we would choose from 5 the first time, 4, the next, 3 after that, and so on, or: Any of the ways we can arrange things, where the order is important. For example, given that we have 5 different colored marbles (blue, green, red, yellow, and purple), if we choose 2 marbles at a time, once we pick the blue marble, the next marble cannot be blue. We can confirm this by listing all the possibilities: 11įor permutations without repetition, we need to reduce the number of objects that we can choose from the set each time. For example, given the set of numbers, 1, 2, and 3, how many ways can we choose two numbers? P(n, r) = P(3, 2) = 3 2 = 9. Where n is the number of distinct objects in a set, and r is the number of objects chosen from set n. When a permutation can repeat, we just need to raise n to the power of however many objects from n we are choosing, so Like combinations, there are two types of permutations: permutations with repetition, and permutations without repetition. Permutations can be denoted in a number of ways: nP r, nP r, P(n, r), and more. In cases where the order doesn't matter, we call it a combination instead. To unlock a phone using a passcode, it is necessary to enter the exact combination of letters, numbers, symbols, etc., in an exact order.

Another example of a permutation we encounter in our everyday lives is a passcode or password. Permutations with Repetition These are the easiest to calculate. No Repetition: for example the first three people in a running race. A phone number is an example of a ten number permutation it is drawn from the set of the integers 0-9, and the order in which they are arranged in matters. Permutations There are basically two types of permutation: Repetition is Allowed: such as the lock above. Home / probability and statistics / inferential statistics / permutation PermutationĪ permutation refers to a selection of objects from a set of objects in which order matters.

Permutations formula