Textbook Question
A __________ is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order.
55
views
4. Probability
Counting
1:21 minutesProblem 5.5.1
Textbook Question
A __________ is an ordered arrangement of r objects chosen from n distinct objects without repetition.
Verified step by step guidance1
Identify the key terms in the problem: 'ordered arrangement', 'r objects', 'n distinct objects', and 'without repetition'.
Recall that when order matters and no repetition is allowed, the concept used is called a 'permutation'.
Understand that a permutation counts the number of ways to arrange r objects out of n distinct objects in order.
The formula for the number of permutations of r objects chosen from n distinct objects is given by: \(P(n, r) = \frac{n!}{(n-r)!}\).
Therefore, the blank in the sentence should be filled with the word 'permutation'.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Permutation
A permutation is an ordered arrangement of objects where the order matters. When selecting r objects from n distinct objects without repetition, the number of permutations counts all possible sequences.
Recommended video:
07:11
Introduction to Permutations
Combination
A combination is a selection of objects where order does not matter. Unlike permutations, combinations count groups without regard to arrangement, which is important to distinguish in problems involving selection.
Recommended video:
05:22Combinations
Without Repetition
Without repetition means each object can be chosen only once in the arrangement. This restriction affects the total number of possible permutations or combinations, as objects are not reused.
Recommended video:
05:15Introduction to the Hypergeometric Distribution
Related Videos
Related Practice