Combination/Problem Solving What is Combination? Combination refers to the selection of objects regardless of their order. That is, changing the order objects does not create a new combination. Formula for the combination of n objects taken r at a time: n! n Cr = n2r20 r!(n-r)! Illustrative Examples: Evaluate: a. 7C2 b. 12C, c. 8C4 + 10C7 8! 10! 7! 8C4 + 10C7 12! 7C2 12C7 = 4!(8-4)!' 7!(10-7)! 2!(7-2)! 7!(12-7)! 8•7•6•5•4! 10 •9.8.7 7•6•5! 12•11•10•9•8•7! 7C2 = 12C7 = 4!(4!) 7!(3!) 2! 5! 42 7! 5! 12•11•10.9.8 7C2 = 12C, = 8•7•6•5•4! 10 •9.8.7 5.4.3•2•1 II
Combination/Problem Solving What is Combination? Combination refers to the selection of objects regardless of their order. That is, changing the order objects does not create a new combination. Formula for the combination of n objects taken r at a time: n! n Cr = n2r20 r!(n-r)! Illustrative Examples: Evaluate: a. 7C2 b. 12C, c. 8C4 + 10C7 8! 10! 7! 8C4 + 10C7 12! 7C2 12C7 = 4!(8-4)!' 7!(10-7)! 2!(7-2)! 7!(12-7)! 8•7•6•5•4! 10 •9.8.7 7•6•5! 12•11•10•9•8•7! 7C2 = 12C7 = 4!(4!) 7!(3!) 2! 5! 42 7! 5! 12•11•10.9.8 7C2 = 12C, = 8•7•6•5•4! 10 •9.8.7 5.4.3•2•1 II
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.1: Counting
Problem 2E: CONCEPTS The number of ways of arranging r objects from n objects in order is called the number of...
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Pls give the answer And solution of the following,I give the illustrative example to help.Thank You;>
Transcribed Image Text:Combination/Problem Solving
What is Combination?
Combination refers to the selection of objects regardless of their order. That is, changing the order of the
objects does not create a new combination.
Formula for the combination of n objects taken r at a time:
n!
n Cr =
ner20
r!(n-r)!
Illustrative Examples:
Evaluate:
а.
7C2
b. 12C7
c. 8C4 + 10C7
8!
10!
8C4 + 10C, =
7!
7C2 =
12!
12C7 =
4!(8–4)!
7!(10–7)!
2!(7-2)!
7!(12–7)!
8•7•6•5•4!
+
10 •9•8•7!
7•6•5!
7C2 =
2! 5!
42
7C2 =
2
%3D
12•11•10•9•8•7!
12C, =
4!(4!)
7!(3!)
7! 5!
12•11•10.9.8
12C7 =
10 •9.8.7!
+
7!(3!)
8•7•6•5•4!
5.4.3•2•1
4!(4!)
95,040
7C2 = 21
12C7 =
8•7•6•5
10 •9.8
120
4.3•2.1
3.2.1
12C7 = 792
1680
720
24
= 70 + 120
Learning Task A: Evaluate the following:
= 190
Transcribed Image Text:Learning Task A: Evaluate the following:
= 190
1. 4C2
2. 10C3
3. 8C6
4. „C4 + 6C5
5. 6C5 • „C4
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