Textbook Question
A __________ is an ordered arrangement of r objects chosen from n distinct objects without repetition.
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4. Probability
Counting
1:04 minutesProblem 5.5.2
Textbook Question
A __________ is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order.
Verified step by step guidance1
Identify the key terms in the problem: 'arrangement of r objects chosen from n distinct objects without repetition and without regard to order.'
Understand that 'without repetition' means each object can be chosen only once, and 'without regard to order' means the order in which objects are chosen does not matter.
Recall the definitions of permutations and combinations: permutations consider order, combinations do not.
Since order does not matter here, the correct term is a 'combination.'
Therefore, the blank should be filled with 'combination,' which is mathematically represented as \(\binom{n}{r} = \frac{n!}{r!(n-r)!}\).
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Combination
A combination is a selection of r objects from a set of n distinct objects where order does not matter and no object is repeated. It counts the number of ways to choose items without regard to arrangement.
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Combinations
Permutation
A permutation is an arrangement of r objects chosen from n distinct objects where order matters and no repetition is allowed. It differs from combinations because the sequence of objects is important.
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07:11Introduction to Permutations
Without Repetition
Without repetition means each object can be selected only once in the arrangement or selection. This restriction affects the total number of possible combinations or permutations.
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05:15Introduction to the Hypergeometric Distribution
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