Permutation (nPr) is the arrangement of objects in a specific order. The order matters in permutations. Combination (nCr) is the selection of objects without regard to order. The order does not matter in combinations.

Example: For the letters A, B, C:

• Permutations of 2 letters: AB, BA, AC, CA, BC, CB (6 results)
• Combinations of 2 letters: AB, AC, BC (3 results)

The formulas are:

Permutation (nPr): P(n, r) = n! / (n - r)!

Combination (nCr): C(n, r) = n! / [r! * (n - r)!]

Where n is the total number of items, r is the number of items selected, and ! denotes factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1 = 120).

Use permutations when:

• The order/arrangement matters (e.g., race results, password combinations)
• Assigning positions (e.g., president, vice-president)
• Arranging distinct objects in sequence

Use combinations when:

• The selection matters but order doesn't (e.g., committee members, lottery numbers)
• Selecting groups where arrangement isn't important
• Choosing subsets from a larger set

Permutations:

• Password and security combinations
• Race results and rankings
• Scheduling and timetables
• Cryptography and encryption

Combinations:

• Lottery and gambling probabilities
• Committee selections
• Menu combinations at restaurants
• Genetics and biological combinations
• Stock portfolio selections