counting II

Complete

Succeeds: counting

Summary

Counting methods
counting_methods.png

Concept

Multiplication principle

  • counting the number of outcomes from experiments performed sequentially

Addition principle

  • counting the number of independent outcome types

Permutation

  • number of ways to arrange objects out of

Combination

  • number of ways to choose objects out of

Application

Forming odd 3-digit numbers without repetition

multiply within a group of outcomes, add between groups

Divide into smaller problems

  • How many ways can 6 persons line up to get on a bus, if 3 persons insist on following one other?
  • Consider the digits 0,1,2,3,4,5 and 6. If each digit can be used at most once, how many 3-digit numbers, which are equal to or greater than 301, can be formed
  • How many ways can 4 men and 3 women sit in a row if no two women are allowed to sit together?

Two dice(unordered)