You are watching: How many ways to arrange 6 letters
The number of ways the a set of things can be i ordered it is known as the variety of permutations of that set. Every distinct setup is dubbed a permutation.
Permutations room computed utilizing factorials. A factorial is a product that a number and all the numbers below it. The factorial the a number is stood for in shorthand utilizing an exclamation point. Because that instance, 6! Is the factorial the 6.
Thus, a set of 6 things have the right to be arranged in (6*5*4*3*2*1) ways, which functions out to 720 ways.
Generally, n! is the variety of permutations of “n” things, vice versa, n!/r! is the number of permutations that “n” points where “r” of them space repeated. Once a set contains recurring elements, the stimulate in i m sorry those elements are i ordered it is important and they deserve to only be arranged in a permutation fairly than a combination.
If a set contains only unique elements, then order does no matter and also in that case, a combination is used. Combinations are teams of numbers the are combined to kind a set. Typically, there room fewer combinations than permutations.
In short, permutations are supplied to arrange item in a list, whereas combine are provided for group items.
In real life, permutations and also combinations have several applications, such as finding the number of ways that an occasion can take place, finding lock codes and also calculating possible lottery combinations.
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