Permutation Formulas and Examples PDF

# PERMUTATION! ## PERMUTATION An arrangement of objects in a definite order or the ordered arrangement of distinguishable objects without allowing repetitions among the objects. ## Preliminary Task Using your scientific calculator, find the value of the following: | | | |---|---| | 1. | 4! =...

# PERMUTATION! ## PERMUTATION An arrangement of objects in a definite order or the ordered arrangement of distinguishable objects without allowing repetitions among the objects. ## Preliminary Task Using your scientific calculator, find the value of the following: | | | |---|---| | 1. | 4! = 24 | | 2. | 3!5! = 720 | | 3. | 7!/5! = 42 | | 4. | 8!/(2!4!) = 840 | | 5. | 7!5!/(3!4!2!) = 2100 | ## What is meant by *n*! (*n* factorial) *n*! = *n*(*n* - 1)(*n* - 2)(*n* - 3)... ## Example: 4! = (4)(3)(2)(1) 4! = 24 ## Types of Permutation 1. Permutation of *n* objects 2. Distinguishable Permutation 3. Permutation of *n* objects taken *r* at a time 4. Circular Permutation ## Permutation of *n* objects *n*P*n* = *n*! (The permutation of *n* objects is equal to *n* factorial) ## How many arrangements are there? 1. Arranging different 3 portraits on a wall 3! = 6 ## How many arrangements are there? 2. Arranging 4 persons in a row for a picture taking 4! = 24 3. Arranging 5 different figurines in a shelf 5! = 120 4. Arranging 6 different potted plants in a row 6! = 720 5. Arranging the digits of the number 123456789 9! = 362 880 6. Arranging the letters of the word CHAIRWOMEN 10! = 3 628 800 ## Distinguishable Permutation P = *n*! / (*p*!*q*!*r*!) There are repeated (or identical) objects in the set. ## How many arrangements are there? 1. Arranging the digits in the number 09778210229 P = 11! / (2!2!2!3!) = 831 600 2. Drawing one by one and arranging in a row 4 identical blue, 5 identical yellow, and 3 identical red balls in a bag P = 12! / (3!4!5!) = 27 720 ## How many arrangements are there? 3. Arranging the letters in the word LOLLIPOP P = 8! / (3!2!2!) = 1680 4. Arranging these canned goods. P = 10! / (3!4!) = 25 200 ## Permutation of *n* objects taken *r* *n*P*r* = *n*! / (*n*-*r*)! Permutation of *n* taken *r* at a time where *n* ≥ *r* ## How many arrangements are there? 1. Choosing 3 posters to hang on a wall from 5 posters you are keeping. *n*P*r* = *n*! / (*n*-*r*)! 5P3 = 5! / (5 - 3)! = 5! / 2! = 60 ## How many arrangements are there? 2. Taking two-letter word, without repetition of letters from the letters of the word COVID *n*P*r* = *n*! / (*n*-*r*)! 5P2 = 5! / (5 - 2)! = 5! / 3! = 20 ## How many arrangements are there? 3. Taking four-digit numbers, without repetition of digits from the number 345678 *n*P*r* = *n*! / (*n*-*r*)! 6P4 = 6! / (6 - 4)! = 6! / 2! = 360 ## How many arrangements are there? 4. Pirena, Amihan, Alena, and Danaya competing for 1st, 2nd, and 3rd places in spoken poetry *n*P*r* = *n*! / (*n*-*r*)! 4P3 = 4! / (4 - 3)! = 4! / 1! = 24 ## How many arrangements are there? 5. Electing Chairperson, Vice Chairperson, Secretary, Treasurer, Auditor, PRO, and Peace Officer from a group of 20 people *n*P*r* = *n*! / (*n*-*r*)! 20P7 = 20! / (20 - 7)! = 20! / 13! = 390 700 800 ## Circular Permutation P = (*n*-1)! ## How many arrangements are there? How many ways can 5 people sit around a circular table? P = (5 - 1)! P = 4! P = 24 ## Other Problems Involving Permutations 1. There are 3 different History books, 4 different English books and 8 different Science books. In how many ways can the books be arranged if books of the same subjects must be placed together? P = 3! 4! 8! 3! P = 34 836 480 ## Other Problems Involving Permutations 2. Three couples want to have their pictures taken. In how many ways can they arrange themselves in a row if couples must stay together? P = 3! 2! P = 12 ## Other Problems Involving Permutations 3. In how many ways can 8 people arrange themselves in a row if 3 of them insist to stay together? P = 6! 3! P = 4 320 ## Other Problems Involving Permutations 4. In how many ways can the letters of the word ALGORITHM be arranged if the vowel letters are placed together? P = 7! 3! P = 30 240 ## Other Problems Involving Permutations 5. In how many ways can the letters of the word TIKTOKERIST be arranged if the consonant letters are placed together? P = 5! 7! / (2! 2! 3!) P = 25 200 ## Other Problems Involving Permutations 6. In how many ways can 7 people be seated around a circular table if 3 of them insist on sitting beside each other? P = (5 - 1)! * 3! P = 144 ## Applications of Permutations 1. Using passwords 2. Using PIN of ATM cards 3. Winning in a contest 4. Electing officers in an organization 5. Assigning of telephone/mobile numbers 6. Assigning plate numbers of vehicles ## Not Applications of Permutations 1. Selecting numbers in a lottery 2. Selecting fruits for salad 3. Choosing members of a committee 4. Using points on a plane to form a polygon (no three points are collinear) ## Thank you Always visit our Facebook group for announcements and updates.