So many cases!

Number Theory Level 2

A 9-digit number that includes every non-zero digit exactly once is chosen at random. What is the probability that it is prime?


The answer is 0.0.

View wiki
Alex Li by Alex Li , 22, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Satyen Nabar
Apr 14, 2015

Sum of the digits is 45 45 , hence divisible by 3 3 . None are prime.

5 Helpful 0 Interesting 1 Brilliant 0 Confused

Moderator note:

Yes. No matter how you arranged the digits, you will always get a sum of digits of 45 45 . By divisibility rule, because 3 ∣ 45 3 \mid 45 , then the 9 digit number is divisible by 3 3 .

Aravind Vishnu
Apr 23, 2015

∑ k = 1 9 k = 45 = 3 × 15. So none will be divisible by 3. \sum_{k=1}^{9}{k}=45=3 \times 15. \text{So none will be divisible by}\, 3.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...