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Permutation & Combination

Calculate arrangements and groups.

r cannot be greater than n
Permutation (nPr)
Order Matters
60
5P3 = 60
Combination (nCr)
Order Doesn't Matter
10
5C3 = 10

Understanding nPr and nCr

Permutation (P)

Permutations are used when the order of selection matters. Arranging people in a line, assigning distinct roles, or creating a password are examples.

Formula:

nPr = n! / (n - r)!

Example: Choosing ABC is different from BAC.

Combination (C)

Combinations are used when the order does not matter. Selecting members for a committee, picking pizza toppings, or choosing lottery numbers are examples.

Formula:

nCr = n! / (r! × (n - r)!)

Example: Choosing ABC is the same as BAC.