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Kenneth Rosen Edition 7 Exercise 6.6 Question 15 (Page No. 438)
Show that the correspondence described in the preamble is a bijection between the set of permutations of $\{1, 2, 3,\dots,n\}$ and the nonnegative integers less than $n!.$
Show that the correspondence described in the preamble is a bijection between the set of permutations of $\{1, 2, 3,\dots,n\}$ and the nonnegative integers less than $n!....
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305
Kenneth Rosen Edition 7 Exercise 6.6 Question 11 (Page No. 438)
Show that Algorithm $3$ produces the next larger $r$-combination in lexicographic order after a given $r$-combination.
Show that Algorithm $3$ produces the next larger $r$-combination in lexicographic order after a given $r$-combination.
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309
Kenneth Rosen Edition 7 Exercise 6.6 Question 7 (Page No. 438)
Use Algorithm $1$ to generate the $24$ permutations of the first four positive integers in lexicographic order.
Use Algorithm $1$ to generate the $24$ permutations of the first four positive integers in lexicographic order.
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310
Kenneth Rosen Edition 7 Exercise 6.6 Question 6 (Page No. 438)
. Find the next larger permutation in lexicographic order after each of these permutations. $1342$ $45321$ $13245$ $612345$ $1623547$ f$23587416$
. Find the next larger permutation in lexicographic order after each of these permutations.$1342$ $45321$ $13245$ $612345$ $1623547$ f$23587416$
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311
Kenneth Rosen Edition 7 Exercise 6.6 Question 5 (Page No. 438)
Find the next larger permutation in lexicographic order after each of these permutations. $1432$ $54123$ $12453$ $45231$ $6714235$ $31528764$
Find the next larger permutation in lexicographic order after each of these permutations.$1432$$54123$$12453$$45231$$6714235$$31528764$
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314
Kenneth Rosen Edition 7 Exercise 6.6 Question 2 (Page No. 438)
Place these permutations of $\{1,2,3,4,5,6\}$ in lexicographic order $:234561, 231456, 165432, 156423, 543216, 541236, 231465, 314562, 432561, 654321, 654312, 435612.$
Place these permutations of $\{1,2,3,4,5,6\}$ in lexicographic order $:234561, 231456, 165432, 156423, 543216, 541236, 231465, 314562, 432561, 654321, 654312, 435612.$
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315
Kenneth Rosen Edition 7 Exercise 6.6 Question 1 (Page No. 438)
Place these permutations of $\{1, 2, 3, 4, 5\}$ in lexicographic order $:43521, 15432, 45321, 23451, 23514, 14532, 21345, 45213, 31452, 31542.$
Place these permutations of $\{1, 2, 3, 4, 5\}$ in lexicographic order $:43521, 15432, 45321, 23451, 23514, 14532, 21345, 45213, 31452, 31542.$
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319
Kenneth Rosen Edition 7 Exercise 6.5 Question 62 (Page No. 434)
How many different terms are there in the expansion of $(x_{1} + x_{2} +\dots + x_{m})^{n}$ after all terms with identical sets of exponents are added?
How many different terms are there in the expansion of $(x_{1} + x_{2} +\dots + x_{m})^{n}$ after all terms with identical sets of exponents are added?
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324
Kenneth Rosen Edition 7 Exercise 6.5 Question 57 (Page No. 434)
How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?
How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?
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325
Kenneth Rosen Edition 7 Exercise 6.5 Question 56 (Page No. 434)
How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?
How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?
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326
Kenneth Rosen Edition 7 Exercise 6.5 Question 55 (Page No. 434)
How many ways are there to distribute six indistinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object?
How many ways are there to distribute six indistinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object?
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327
Kenneth Rosen Edition 7 Exercise 6.5 Question 54 (Page No. 434)
How many ways are there to distribute five indistinguishable objects into three indistinguishable boxes?
How many ways are there to distribute five indistinguishable objects into three indistinguishable boxes?
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328
Kenneth Rosen Edition 7 Exercise 6.5 Question 53 (Page No. 434)
How many ways are there to put six temporary employees into four identical offices so that there is at least one temporary employee in each of these four offices?
How many ways are there to put six temporary employees into four identical offices so that there is at least one temporary employee in each of these four offices?
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330
Kenneth Rosen Edition 7 Exercise 6.5 Question 51 (Page No. 434)
How many ways are there to distribute six distinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object?
How many ways are there to distribute six distinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object?
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