Here are the essential concepts you must grasp in order to answer the question correctly.
Permutations
Permutations refer to the different arrangements of a set of objects where the order matters. When calculating permutations of n distinct objects taken r at a time, you are counting the number of ways to arrange r objects selected from a total of n. For example, if you have three distinct letters A, B, and C, the permutations of 2 letters taken from these would include AB, AC, BA, BC, CA, and CB, totaling six arrangements.
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Introduction to Permutations
Factorial
The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers up to n. It is a fundamental concept in combinatorics used to calculate permutations and combinations. For instance, 4! equals 4 × 3 × 2 × 1 = 24, which represents the total arrangements of four distinct objects.
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Combination vs. Permutation
While both permutations and combinations deal with selecting items from a set, the key difference lies in the importance of order. Permutations consider the arrangement of selected items as significant, whereas combinations focus solely on the selection itself, disregarding order. For example, selecting the letters A and B is the same in combinations (AB) but different in permutations (AB vs. BA).
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Permutations vs. Combinations
3:27 minutes
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