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Aabhyas on Permutation and combinations |Class 11 maths | @Integralganit


Permutations and combinations are mathematical concepts for counting arrangements and selections from a set, differing by the importance of order: Permutation (P) is for arrangements where order matters (like a lock combination 4-7-2), calculated as nPr = n! / (n-r)!, while Combination (C) is for selections where order does not matter (like a fruit salad with apples, grapes, and bananas), calculated as nCr = n! / (r! * (n-r)!).
Permutations
Definition: A permutation is an arrangement of elements where the order of selection is important.
Key Idea: Each different order of the same items counts as a distinct permutation.
Example: If you are arranging letters in a word, the order matters. "CAT" is a different permutation than "ACT".
Formula: The number of permutations of n items taken r at a time is given by P(n, r) = n! / (n - r)!.
Combinations
Definition: A combination is a selection of elements from a set where the order of selection does not matter.
Key Idea: Different orders of the same items are considered the same combination.
Example: Choosing a group of friends from a class or selecting ingredients for a salad are combinations because the order in which you choose them doesn't change the group or salad itself.
Formula: The number of combinations of n items taken r at a time is given by C(n, r) = n! / (r! * (n - r)!).
Key Difference in Summary
Permutations: Think "ordered." If the order of the items changes the outcome, it's a permutation.
Combinations: Think "unordered." If the order of the items doesn't matter, it's a combination