Lance Escanlar

• Permutation


  Arranging things in different order
• Combination


  Combining things where the order does not matter
• Permutation example


  • a b c
  • c a b
• The number of permutations of a b c is 2
• The number of combinations of a b c is 1
• The number of permutations of choosing 2 out of 4 letters a b c d is 12
• The number of combinations of choosing 2 out of 4 letters a b c d is 6
• n P r


  Formula to calculate permutations: n! / (n-r)!
• n C r


  Formula to calculate combinations: n! / (n-r)! * r!
• Calculating permutations


  1. n = 4, r = 2

  2. 4! / (4-2)! = 12
• Calculating combinations


  1. n = 4, r = 2

  2. 4! / (4-2)! * 2! = 6
• Arranging 3 books from a group of 7 is a permutation
• Calculating permutations of 3 books from 7

  7! / (7-3)! = 210
• Arranging 5 books on a shelf is a permutation
• Calculating permutations of 5 books

  5 * 4 * 3 * 2 * 1 = 120
• Choosing 4 teams from a pool of 12 engineers is a combination
• Calculating combinations of 4 from 12


  12! / (12-4)! * 4! = 495
• Arranging the letters in the word 'alabama' is a permutation
• Arranging the letters in the word 'mississippi' is a permutation