#Permutation order matters series#

If you are looking for 'at least 2 Heads', 2 options match: HHH and HHT (order not important). These are (because order is not important): HHH, HHT, HTT, TTT If the question is 'If you throw a 2-sided coin (N=2), R times, how many times can you get at least 2 heads?', you are looking for Combination (order is not important) with Repetition where 'HHT' and 'THH' are same outcomes (combination).Ĭombination with Repetition formula is the most complicated (and annoying to remember): (R+N-1)! / R!(N-1)!įor 3 2-sided coin tosses (R=3, N=2), Combination with Repetition: (3+2-1)! / 3!(2-1)! = 24 / 6 = 4 Probability of 'at least 2 heads in a row' is 3/8th (0.375) To help you to remember, think ' P ermutation. So, we should really call this a 'Permutation Lock' In other words: A Permutation is an ordered Combination. In these, 'at-least-2 Heads in a row' permutations are: HHH, HHT, THH - 3. When the order does matter it is a Permutation. Permutation with Repetition is the simplest of them all:ģ tosses of 2-sided coin is 2 to power of 3 or 8 Permutations possible. To calculate a permutation, you will need to use the formula n P r n / ( n - r ). 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.

#Permutation order matters series#

If the question is 'How many ways a series of R coin tosses (N=2 sides) can go? Of these, how many will have 2 Heads in the row?', you are looking for Permutation with Repetition where 'HHT' is different outcome from 'THH'. A permutation is a method to calculate the number of events occurring where order matters. A permutation is a way to select a part of a collection, or a set of things in which the order matters and it is exactly these cases in which our permutation calculator can help you. *Probably the best page that summarizes the Combination vs Premutation with or without Repetition * Coin toss series can be viewed, depending on what you want to know, as either 'combination' or 'permutation' but in all cases 'with repetition' (meaning same side can occur again and again).