Question
A sequence where order distinguishes one sequence of things from another order of the same things is called a permutation. Suppose we have thigs a,
A sequence where order distinguishes one sequence of things from another order of the same things is called a permutation. Suppose we have thigs a, b, and c. Drawing without replacement 3 times produces the permutations {abc, acb, bac, bca, cab, and cba}. We see 3 things have 6 permutations or orders. Lets generalize. For a sequence of n things drawn from N things without replacement, there are N ways the 1st draw occurs. For each of the N outcomes of 1st draw, there are N-1 ways the 2nd draw can occur. So, for 2 draws, there are Nx(N-1) possible permutations. Continuing, there are Nx(N-1)x(N-2) permutations for 3 draws. In general, its Nx(N-1)xN-2)xx(N-n+1)=N!/(N-n)!, or using Excel functions, =PERMUT(N,n); ! is read factorial; Example: 6! = 6x5x4x3x2x1. How many sequences of 3 things can be formed from 7 different things with replacement and order is important?
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