Kenneth Rosen Edition 7 Exercise 6.5 Question 41 (Page No. 433)

In this exercise we will prove Theorem $2$ by setting up a one-to-one correspondence between the set of $r$-combinations with repetition allowed of $S = \{1, 2, 3,\dots,n...

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Kenneth Rosen Edition 7 Exercise 6.5 Question 48 (Page No. 433)
Prove Theorem $4$ by first setting up a one-to-one correspondence between permutations of $n$ objects with $n_{i}$ indistinguishable objects of type $i,\; i = 1, 2, 3,\dots, k,$ and the distributions of $n$ objects in $k$ boxes such that $n_{i}$ objects are placed in box $i,\: i = 1, 2, 3,\dots,k $ and then applying Theorem $3.$

Prove Theorem $4$ by first setting up a one-to-one correspondence between permutations of $n$ objects with $n_{i}$ indistinguishable objects of type $i,\; i = 1, 2, 3,\do...

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Kenneth Rosen Edition 7 Exercise 6.5 Question 47 (Page No. 433)
Use the product rule to prove Theorem $4,$ by first placing objects in the first box, then placing objects in the second box, and so on.

Use the product rule to prove Theorem $4,$ by first placing objects in the first box, then placing objects in the second box, and so on.

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Kenneth Rosen Edition 7 Exercise 6.5 Question 46 (Page No. 433)
A shelf holds $12$ books in a row. How many ways are there to choose five books so that no two adjacent books are chosen? [Hint: Represent the books that are chosen by bars and the books not chosen by stars. Count the number of sequences of five bars and seven stars so that no two bars are adjacent.]

A shelf holds $12$ books in a row. How many ways are there to choose five books so that no two adjacent books are chosen? [Hint: Represent the books that are chosen by ba...

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discrete-mathematics
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combinatory
descriptive

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