What is the difference between combination snd permutations in Elementary math??
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In elementary math, permutations and combinations are both ways to count the number of possible outcomes. The difference between permutations and combinations lies in whether the order of the items being counted matters.
Permutations:
Permutations are counting arrangements where the order of the items matters. In other words, different arrangements of the same items are considered as distinct outcomes. For example, consider the letters A, B, and C. If you were to list all the permutations of these letters, you would get: ABC, ACB, BAC, BCA, CAB, CBA. Each of these arrangements is distinct because the order of the letters is different.
To calculate the number of permutations, you often use the formula nPr = n! / (n - r)!, where n is the total number of items and r is the number of items to be chosen and arranged.
Combinations:
Combinations, on the other hand, are counting selections where the order does not matter. In other words, different selections of the same items are considered as equivalent outcomes. For example, let's say you have three books, A, B, and C. If you want to select two books from this set, the combinations would be AB, AC, and BC. Notice that the order of the books does not matter in combinations; AB is the same as BA.
To calculate the number of combinations, you often use the formula nCr = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to be chosen.
In summary, permutations consider the order of items, while combinations do not.