# Thread: arrange book's question

1. ## arrange 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

2. What is that supposed to mean?. I am sorry, but it makes no sense.

3. Hello, neworld222!

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

places on at will the bookshelf 10 books,
asks 5 books which in which assigns to put on the same place probability
I'll take a wild guess . . .

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 $10!$ possible arrangements.

Duct-tape those five books together.
Then we have six "books" to arrange: . $\left\{\boxed{ABCDE},\,F,\,G,\,H,\,I,\,J\right\}$
. . They can be arranged in $6!$ ways.

For each of these, the five books can be permuted in $5!$ ways.
. . Hence, there are: . $(6!)(5!)$ desirable arrangements.

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

4. Originally Posted by Soroban
Hello, neworld222!

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

I'll take a wild guess . . .

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 $10!$ possible arrangements.

Duct-tape those five books together.
Then we have six "books" to arrange: . $\left\{\boxed{ABCDE},\,F,\,G,\,H,\,I,\,J\right\}$
. . They can be arranged in $6!$ ways.

For each of these, the five books can be permuted in $5!$ ways.
. . Hence, there are: . $(6!)(5!)$ desirable arrangements.

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

yes ,you give what i need .English is not my first lanuage,so i sorry for that i made you take a wild guess