places on at will the bookshelf 10 books, asks 5 books which in which assigns to put on the same place probability

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- Jun 28th 2007, 11:47 PMneworld222arrange book's question
places on at will the bookshelf 10 books, asks 5 books which in which assigns to put on the same place probability

- Jun 29th 2007, 05:48 AMgalactus
What is that supposed to mean?. I am sorry, but it makes no sense.

- Jun 29th 2007, 08:04 AMSoroban
Hello, neworld222!

I think it's Yoda, the Jedi Master . . .

Quote:

places on at will the bookshelf 10 books,

asks 5 books which in which assigns to put on the same place probability

Ten distinct books are placed randomly on a shelf (in a row).

What is the probability that a particular five books are adjacent?

There are $\displaystyle 10!$ possible arrangements.

Duct-tape those five books together.

Then we have six "books" to arrange: .$\displaystyle \left\{\boxed{ABCDE},\,F,\,G,\,H,\,I,\,J\right\}$

. . They can be arranged in $\displaystyle 6!$ ways.

For each of these, the five books can be permuted in $\displaystyle 5!$ ways.

. . Hence, there are: .$\displaystyle (6!)(5!)$ desirable arrangements.

The probability is: .$\displaystyle \frac{(6!)(5!)}{10!} \;=\;\frac{1}{42}$

- Jun 30th 2007, 01:49 AMneworld222