MATH

• Permutation


  The different possible arrangements of a set of objects
• Methods to illustrate permutation

  1. Listing

  2. Tree diagram

  3. Table

  4. Fundamental counting principle
• Examples of permutation


  • Arranging shoes on a shoe rack
  • Creating password for ATM card
  • Combination lock
• Rosa has 4 new blouses (stripes, ruffles, long sleeve, sleeveless) and 3 skirts (red, pink, black)
• Illustrating permutation of blouse and skirt combinations


  1. Listing

  2. Tree diagram

  3. Table

  4. Fundamental counting principle
• The number of possible blouse and skirt combinations is 12
• If Rosa has 5 blouses and 4 skirts, the number of possible outfits is 20
• Combinations


  An arrangement of n objects with no repetitions and the order is not important
• Example problems involving combinations


  • Choosing a committee of 5 persons from a group of 7
  • Drawing a hand of 13 cards with 10 spades from a deck
  • Choosing 6 numbers from 1 to 42 in no particular order
• Combination of n objects taken r at a time can be represented as nCr
• Evaluating combinations


  • Combination of 7 taken 4 = 7! / (7-4)! * 4! = 35
  • Combination of 15 taken 3 = 15! / (15-3)! * 3! = 455
  • Choosing 3 teachers from 30 to attend a conference = 30! / (30-3)! * 3! = 4060
• Handshakes between 6 officers

  • Combination of 6 taken 2 = 6! / (6-2)! * 2! = 15 handshakes
• Combinations in a 6/42 lotto game

  • 42 choose 6 = 42! / (42-6)! * 6! = 5,245,786 possible bets
• Choosing a committee of 4 from 10 persons

  • Combination of 10 taken 4 = 210 ways
• Choosing a committee of 5 from 7 single ladies and 9 men


  • No gender restriction: 16 choose 5 = 4,368 ways
  • 3 single ladies and 2 men: (7 choose 3) * (9 choose 2) = 1,260 ways
  • All single ladies: 7 choose 5 = 21 ways
• Inspecting a carton of 20 CDs with 5 pirated and 15 original

  • 1 pirated CD: 5 choose 1 * 15 choose 2 = 525 ways
  • 2 pirated CDs: 5 choose 2 * 15 choose 1 = 150 ways
  • All original CDs: 15 choose 3 = 455 ways
• In a class of 20, there are 1,140 ways the students can retreat for a field trip
• If Michael is not allowed, there are 969 ways the students can retreat
• If Derek must answer 5 out of 10 questions, there are 252 ways he can choose the questions
• Using 6 points, with 3 not collinear, there are 15 different lines that can be drawn
• From 10 freshmen and 5 sophomores, there are 2,100 ways to form a committee of 4 freshmen and 2 sophomores