# Simple understanding question

1. Feb 23, 2010

### annoymage

1. The problem statement, all variables and given/known data

Given a random permutation of integer in the set (1,2,3,4,5), let X equal the number of integer that are in their natural position.

3. The attempt at a solution

i don't understand "number of integer that are in their natural position"

2. Feb 23, 2010

### Dick

It's the number of integers that are mapped to themselves under the random permutation.

3. Feb 23, 2010

### annoymage

hmm still confused, im sorry for my bad english,

let me tell what i understand,

the universal set are

(1,2,3,4,5),(5,4,3,2,1),(1,2,3,5,4) and so on,
there's 5!=120 in total,

so, which are integer that maps to itself? can give me some example.. :)

4. Feb 23, 2010

### swuster

If, for example, your permutation is (2,3,1,4,5) then X = 2 because 4 and 5 are in their original, or natural positions.

5. Feb 23, 2010

### annoymage

OOOOOOOOOOOOOOOOOOOOOOOO, i get it, thankssss,
thank you very much

6. Feb 24, 2010

### snshusat161

But what about 3 and 1

7. Feb 24, 2010

### annoymage

he means, that, 4 and 5 is the integer in its natural position...
so, x=2 which means, there are two integer in its natural position..

(2,3,1,*,*) is not in their natural position because (1,2,3,*,*) is their actual position

example:

(5,2,3,4,1) , so 2,3, and 4 are in thier natural position, so x=3

8. Feb 24, 2010

### snshusat161

Thank, I got it.