Formula Difference between the two formulae: Use the calculator to find the values of permutations and combinations. Selection of menu, food, clothes, subjects, teams, … Keywords: Select, choice,… Ģ. Keywords: Arrangements, arrange,… Order is not important. Arranging people, digits, numbers, alphabets, letters, colours, … 3. ĭIFFERENCES BETWEEN PERMUTATIONS AND COMBINATIONS PERMUTATIONS COMBINATIONS 1. Compare and Contrast between Permutations and Combinations. W3 M3, or W4 M2, 4 C 3 X 3 C 3 + 4 C 4 X 3 C 2 = 7ĬONCLUSIONS 1. Find the number of ways at least 3 women are chosen. import local 3 17 2 9 3 C 2 17 C 9 = 72930 r nĬondition Combination 2 A committee consisting of 6 members is to be chosen from 3 men and 4 women. Find the number of ways the main player can be chosen.
Eleven main players are to be chosen with the condition that it must consist of 2 imported players. N = 4 Choose 1: A B C D A B C D Choose 2: A B A C A D B C Choose 3: A B C A C D B C D B D C D A B D Choose 4: A B C D = 4 = 4 C 1 = 6 = 4 C 2 = 4 = 4 C 3 = 1 = 4 C 4Ĭonditional Combination 1 A football team has 17 local players and 3 imported players. of arrangements with two E next to each other Complimentary Methods Use: The number of arrangements of event A = Total arrangements – arrangement of A’ A A’ SĮxample Find the number of the arrangement of all nine letters of word SELECTION in which the two letters E are not next to each other.
To arrange PENALTY such that vowels are side by side 1 2 3 4 5 6 ģ. Ī E A E P N L T Y P N L T Y A E 6 ! 2! = 1440 4. Questions related to Forming Numbers with digits and conditions Use Multiplication Rules Conditions : Sit side by side, next to each other – group together and consider as 1 object for arranging with other objects, make sure remember the arrangement of the grouped objects itself. is filled first W R L D C P O O U 2 7 6 5 4 U =1680įind the number of ways to form 6 letter word from the letters B, E, C, K, H, A, M with the condition that it must starts with a consonant. Questions related to Forming Numbers with digits and conditions Use Multiplication Rules Ĭondition 1 Find the number of ways to form 5 letter word from the letters W, O,R, L, D, C, U, P with the condition that it must starts with a vowels. 8 x 7 x 6 x 5 x 4 = 6720Ĩ choices 7 choices 6 choices 5 choices 4 choices number of ways to arrange r from n objects n (n-1) (n-2) (n-3) (n-(r-1))ġ. Permutation Number of ways to arrange r objects from n objects Ĩ choices 7 choices 6 choices 5 choices 4 choices Number of ways to arrange 5 students from 8 students. To arrange 12 finalists 12 different objects = 12 !ĭNA 23 pairs of chromosomes 23 ! different ways to arrange To arrange digits 2, 5, 6, 8 = 4 ! 4 different objects 3. To arrange 10 different objects = 10 ! 2. Number of ways to arrange 4 different objects A B C D B C D 24 A B C D A B C D A B C D A B C D A B C D A B C D Number of ways to arrange 3 different objects A B C A B C B B A C C A C A B C B A 6 ways A B C Permutation Number of ways to arrange n different objects Keywords: Arrangements, arrange,… Selection of menu, food, clothes, subjects, teams. Tom & Jerry Jerry & Tom They are the same cat & the mouse OR How many combinations? 1 COMBINATIONĭIFFERENCES BETWEEN PERMUTATIONS AND COMBINATIONS PERMUTATIONS COMBINATIONS Arranging people, digits, numbers, alphabets, letters, colours. Tom & Jerry Jerry & Tom How many arrangements? 2 PERMUTATIONS Combination – grouping,selection ChoicesĬombination Arrangement is not important X Y Or X Y Are the same one combination PERMUTATION Permutation – the arrangement is important How many ways can the letter X and Y be arranged? X Y X Y There are two ways two different permutationĬOMBINATIONS In Combinations, we do not arrange the selections in order. Permutation – variation, order Arrangement
Each different order represents a different outcome. PERMUTATION In permutation, the order of the objects or outcomes is important. Multiplication Rule/Principle Adidas Reebox Nike 10 23 7 9 2 3 4 24 = The number of ways the outfit can be chosen = MULTIPLICATION RULE If an operation can be performed in r different ways and a second operation can be performed in s different ways, then both the operations can be performed successively in r x s ways.
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