how many permutations can be formed from k types of objects with n sub i >...
how many permutations can be formed from k types of objects with n sub i > 0 objects of type i for 1 <= i <= k so that all objects of the same type are adjacent to each other in each permutation
Homework Answers
ANSWER::
Answer:
A bundle of two specific things can be put in r places in (r-1) ways and 2 things in the bundle can be arranged themselves into 2! ways. Now (n-2) things will be arranged in (r-2) places in n-2Pr-2 ways.
thus using the fundamental principle of counting, the required number of permutations will be 2!.(r-1).n-2Pr-2
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how many permutations can be formed from k types of objects with
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9 Word Permutation How many different to letter permutations can be written from the word berayon?
9 Word Permutation How many different to letter permutations can be written from the word berayon?
How many permutations can be formed by sampling 5 things from 6 different things without replacement?
How many permutations can be formed by sampling 5 things from 6 different things without replacement?
How many permutations are there and show steps to how to get the answer in that...
How many permutations are there and show steps to how to get the
answer in that form with permutation calculation
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3) (10 pts) For the purposes of this question, a permutation of size n is any...
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Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 < i S n 1 such that p, > Pi+1. How many permutations in Sn have exactly one des...
Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 < i S n 1 such that p, > Pi+1. How many permutations in Sn have exactly one descent?
Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 Pi+1. How many permutations in Sn have exactly one descent?
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4. Here is a fact about permutations: (*) nPr= n!/(n-k)!, for all k =n. Let's prove this via mathematical induction for the fixed case k-3. 2 of 3 (i) Write clearly the statement (**) we wish to prove. Be sure your statement includes the phrase "for all n" (ii) State explicitly the assumption in (*) we will thus automatically make about k-2 (ii) Now recall that to prove by induction means to show that IfmPm!/lm-k)! is true for all km...
2. Consider the permutations a (123)(45) and b (2543) in the symmetric group S (a) Compute the co...
2. Consider the permutations a (123)(45) and b (2543) in the symmetric group S (a) Compute the conjugate permutation ca using (i) the definition a-b ab (b) What is the order of a? How many permutations have the same shape as a; that is, (x x x)(x x). (c) What is the subgroup H of all permutations in Ss that commute with the permutation a? d) Using the result of the previous part, or otherwise, find 5 other permutations bi,...
A legislative committee consists of 7 Democrats and 9 Republicans. A delegation of 3 is to...
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How many permutations of three items can be selected from a group of six
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How many permutations are there and show steps to how to get the
answer in that form with permutation calculation
home. Assume that she walks only east or south 18. Nadia's office is four blocks east aa three when going from home to work. Ue Pascal's method to deternine how many different routes Nadia can take. 13 35 eyyoa b) Use a permutation calculation to determine how many different routes Nadia cah take [2]1 20
3) (10 pts) For the purposes of this question, a permutation of size n is any ordering of the integers 0, 1, 2, ..., n-1. We define a spaced-out permutation of size n to be a permutation such that two consecutive terms in the permutation differ by at least 2. For example, [0, 2, 4, 1, 3] is a spaced out permutation of size 5, and [5, 2, 4, 0, 3, 1] is a spaced out permutation of size 6,...
Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 < i S n 1 such that p, > Pi+1. How many permutations in Sn have exactly one descent?
Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 Pi+1. How many permutations in Sn have exactly one descent?
4. Here is a fact about permutations: (*) nPr= n!/(n-k)!, for all k =n. Let's prove this via mathematical induction for the fixed case k-3. 2 of 3 (i) Write clearly the statement (**) we wish to prove. Be sure your statement includes the phrase "for all n" (ii) State explicitly the assumption in (*) we will thus automatically make about k-2 (ii) Now recall that to prove by induction means to show that IfmPm!/lm-k)! is true for all km...
2. Consider the permutations a (123)(45) and b (2543) in the symmetric group S (a) Compute the conjugate permutation ca using (i) the definition a-b ab (b) What is the order of a? How many permutations have the same shape as a; that is, (x x x)(x x). (c) What is the subgroup H of all permutations in Ss that commute with the permutation a? d) Using the result of the previous part, or otherwise, find 5 other permutations bi,...
A legislative committee consists of 7 Democrats and 9 Republicans. A delegation of 3 is to be selected to visit a small island republic. Complete parts (a) through (d) below. (a) How many different delegations are possible? The 3 delegates can be selected different ways. The number of possible permutations is 36036 If the n objects in a permutations problem are not all distinguishable—that is, if there are ny of type 1, n2 of type 2, and so on, for...
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