SOLUTION: There are 9! ways to arrange the digits 1-9 to form a 9-digit number. If you know this, then if you wrote all 9! possibilities on cards (1 way per card), and asked your friend to s

Algebra.Com
Question 1049339: There are 9! ways to arrange the digits 1-9 to form a 9-digit number. If you know this, then if you wrote all 9! possibilities on cards (1 way per card), and asked your friend to select one at random; what is the probability that the number he/she selected is prime?
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
There are 9! ways to arrange the digits 1-9 to form a 9-digit number. If you know this, then if you wrote all 9! possibilities on cards
(1 way per card), and asked your friend to select one at random; what is the probability that the number he/she selected is prime?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The probability is 0 (zero). 

All these numbers (all and each of 9! numbers) are divisible by 3.
Each is a multiple of 3.

Apply the divisibility rule by 3.

The sum of all digits in each of these 9-digit numbers is

1 + 2 + 3 + . . . + 9 =  = 45 

is divided by 3.

Thank you for this joke problem.

Good entertainment !


For divisibility rules see the lessons
    - Divisibility by 2 rule,
    - Divisibility by 3 rule,
    - Divisibility by 4 rule,
    - Divisibility by 5 rule,
    - Divisibility by 6 rule,
    - Divisibility by 9 rule,
    - Divisibility by 10 rule,
    - Divisibility by 11 rule,
    - Restore the omitted digit in a number in a way that the number is divisible by 9  and
    - Restore the omitted digit in a number in a way that the number is divisible by 11.
in this site.


RELATED QUESTIONS

Arranging digits. In how many ways can you arrange the digits 8,7,6 and 3 to form a... (answered by stanbon)
In how many ways can you arrange the digits 8, 7, 6, and 3 to form a four-digit number... (answered by Edwin McCravy)
How many ways are there to write a three digit positive integer using the digits 1 3 7 &... (answered by solver91311)
The sum of the digits of a two digit number is 9. If 9 is added to the number, then the... (answered by Edwin McCravy,AnlytcPhil)
My ID number is quite remarkable. It's a 9-digit number with the digits 1-9 appearing... (answered by bucky)
A phone number has 7 digits in it from 0 to 9. In how many ways can you arrange the 7... (answered by Alan3354)
if you wrote all of the whole numbers from 1 to 100 which digit 0-9 would you write the... (answered by Edwin McCravy)
1.In how many different ways can 6 classes be scheduled during a 6-period day? 2.In how... (answered by stanbon)
Please help me with this problem: Arrange the digits form 1 through 9 to from a single... (answered by checkley77)