Explanation Approach: The number of combinations of n distinct objects taken r at a time is, C ( n , r ) = n ! r ! ( n − r ) ! Here, ( r ≤ n ) Calculation: Notice that the number of ways of selecting two objects from ten objects is similar to the number of ways of rejecting eight objects from ten objects. The number of ways of selecting 2 objects from 10 objects is C ( 10 , 2 ) , and the number of ways of rejecting eight objects from is 10 objects is C ( 10 , 8 )

4th Edition

ISBN: 2818000007824

Author: Stewart

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

Videos

Question

Chapter 14.1, Problem 92E

To determine

To explain:

The reason that the number of ways of selecting two objects from ten objects is same as the number of ways of selecting eight objects from ten objects, and C(n,r)=C(n,n−r).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.1, Problem 91E

Chapter 14.1, Problem 93E

Students have asked these similar questions

Solve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8

5. Solve for the matrix X. (Hint: we can solve AX -1 = B whenever A is invertible) 2 3 0 Χ 2 = 3 1

Write p(x) = 6+11x+6x² as a linear combination of ƒ (x) = 2+x+4x² and g(x) = 1−x+3x² and h(x)=3+2x+5x²

Chapter 14 Solutions

ALGEBRA AND TRIGONOMETRY-WEBASSIGN

Ch. 14.1 - CONCEPTS The Fundamental Counting Principle says...Ch. 14.1 - CONCEPTS The number of ways of arranging r objects...Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The reason that the number of ways of selecting two objects from ten objects is same as the number of ways of selecting eight objects from ten objects, and C ( n , r ) = C ( n , n − r ) .

Solution Summary: The author explains that the number of ways of selecting two objects from ten objects is the same as those of rejecting eight objects.

Concept explainers

Videos

To explain:

The reason that the number of ways of selecting two objects from ten objects is same as the number of ways of selecting eight objects from ten objects, and C(n,r)=C(n,n−r).

Want to see the full answer?

Chapter 14 Solutions

The reason that the number of ways of selecting two objects from ten objects is same as the number of ways of selecting eight objects from ten objects, and C ( n , r ) = C ( n , n − r ) .

Solution Summary: The author explains that the number of ways of selecting two objects from ten objects is the same as those of rejecting eight objects.

Concept explainers

Videos

To explain: The reason that the number of ways of selecting two objects from ten objects is same as the number of ways of selecting eight objects from ten objects, and C(n,r)=C(n,n−r).

Want to see the full answer?

Chapter 14 Solutions

To explain:

The reason that the number of ways of selecting two objects from ten objects is same as the number of ways of selecting eight objects from ten objects, and C(n,r)=C(n,n−r).