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Questions and Answers
What is the formula for the total number of permutations of p1 things alike of one kind, p2 alike of a second kind, and so on, up to pk things alike?
What is the formula for the total number of permutations of p1 things alike of one kind, p2 alike of a second kind, and so on, up to pk things alike?
What is the number of circular permutations of n different things taken all at a time?
What is the number of circular permutations of n different things taken all at a time?
How is the number of combinations of n distinct objects taken r at a time calculated when k specific objects always occur?
How is the number of combinations of n distinct objects taken r at a time calculated when k specific objects always occur?
What is the total number of selections of one or more objects from n different objects?
What is the total number of selections of one or more objects from n different objects?
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What is the correct expression for the number of combinations of n distinct objects taken r at a time when k specific objects never occur?
What is the correct expression for the number of combinations of n distinct objects taken r at a time when k specific objects never occur?
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What is the result of the sum $inom{n}{0} + inom{n}{1} + inom{n}{2} + insom{n}{3} + insom{n}{n}$?
What is the result of the sum $inom{n}{0} + inom{n}{1} + inom{n}{2} + insom{n}{3} + insom{n}{n}$?
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How do you calculate the number of ways to form a necklace of n dissimilar beads?
How do you calculate the number of ways to form a necklace of n dissimilar beads?
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What represents the number of circular permutations of n different things taken r at a time?
What represents the number of circular permutations of n different things taken r at a time?
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Study Notes
Permutations and Combinations
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Identical Objects: If 'p' things are alike of one kind, 'p₂' alike of a second kind, and so on, the number of permutations is (p₁+p₂+p₃...+pₖ)! / (p₁! p₂! p₃!...pₖ!)
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Circular Permutations: The number of circular permutations of 'n' different things taken all at once is (n-1)!
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Necklace Formation: Number of ways to form a necklace with 'n' dissimilar beads is (n-1)! / 2
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Circular Permutations (r taken at a time): Formula for circular permutations of n different items taken r at a time is not provided.
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Combinations with Restrictions:
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If k particular objects always occur in a combination of n distinct objects taken r at a time (0 ≤ k ≤ r), the number of combinations is n-kCr-k.
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If k objects never occur in a combination of n distinct objects taken r at a time (1 ≤ k ≤ r), the number of combinations is n-kCr.
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Total Selections: The total number of selections of one or more objects from n different objects is 2ⁿ - 1 = nC₁ + nC₂ + nC₃ +...+ nCn
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Description
Test your knowledge on permutations and combinations with this quiz. Explore topics such as identical objects, circular permutations, and combinations with restrictions. Enhance your understanding of these important concepts in probability and combinatorics.
