![]() Probability of you getting at least 2 heads is 2 outcomes / 4 Combinations (with Repetition) = 0.5. 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 As you may recall from school, a combination does not take into account the order, whereas a permutation does. While Im at it, I will examine combinations and permutations in R. ![]() 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 Time to get another concept under my belt, combinations and permutations. Probability of "at least 2 heads in a row" is 3/8th (0.375) In these, "at-least-2 Heads in a row" permutations are: HHH, HHT, THH - 3. 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. 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". ![]() ![]() The number of distinct combinations of 3 professors is 73 63 35 3321 6 73 73 7 7 6 5 210 73 () PP C 7C 3 is the number combinations of 3 objects chosen from a set of 7. *Probably the best page that summarizes the Combination vs Premutation with or without Repetition * Combinations: 7C3 In our list of 210 sets of 3 professors, with order mattering, each set of three profs is counted 3 6 times.
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