Permutations
Chapter Name : Permutations And Combinations |
Sub Topic Code : 104_11_07_03_02 |
Topic Name : Permutations |
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Sub Topic Name : Factorial Notation |
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Introduction
• As we know the expression of permutation nPr is lengthy so to reduce the size of this expression the notation factorial is used. • Factorial of a number is the product of all numbers from 1 to that number. • Factorial of a number is denoted by n!
Pre-Requisites:
• Knowledge of fundamental principle of counting. • Knowledge of permutations.
Activity:
By looking at the colors of the blocks one at a time you can observe how many blocks of each color there is in a factorial.
Real Life Question:
In how many different ways you can order pizza with cheese topping?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Permutations | Permutation is an arrangement of number or object in definite order. |
| Factorial | Product of all numbers from 1 to that number. |
| Whole numbers | Whole numbers are simply the numbers from 0, 1, 2… |
| Natural numbers | Natural numbers are all counting numbers from 1, 2, 3… |
| Irrational numbers | Numbers which cannot be written as fractions like pi, square root. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Blocks | Make a tower of blocks and take different colors for numbers1 to 9. |
Real life uses :
Factorials are used in many computer applications. Permutations are the biggest use of factorial.
Places to visit :
Look for 5 Lunch boxes and 3 fruits. In how many different ways can you arrange fruits in 5 Lunch boxes?
Practical examples around us
| Examples | Explainations |
|---|---|
| In how many ways you can vote for your school elections for captain and vice-captain from a group of 5 selected candidates? | This question is asking us to select 2 persons from a group of 5.Here n= 5 and r=2. |
What you learn in Theory:
Factorials simplify the permutation formula.
What you learn in Practice:
Factorial calculates the possible outcomes of events. For example how many possible outcomes of running race and how many combinations of first, second and third racers.