Question 1094960
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A 9 digit number using the digits 1,2,3,4,5,6,7,8,9 is written randomly without repetition. 
Find the probability that number will me divisible by 9 ?
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<U>Answer</U>.  This probability is equal to 1.


<U>Solution</U>


<pre>
The rule of divisibility by 9 says:


    Integer number is divisible by 9 if and only if the sum of its digits is divisible by 9.


For 9-digit number, written with the digits  1, 2, 3, 4, 5, 6, 7, 8, 9 (each digit is used and each digit is used only once) the sum of digits is

    1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45,

which is divisible by 9 for each and every permutation of these digits.


Hence, any such number is divisible by 9.
</pre>

On divisibility rules see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-2-rule.lesson>Divisibility by 2 rule</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-3-rule.lesson>Divisibility by 3 rule</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-4-rule.lesson>Divisibility by 4 rule</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-5-rule.lesson>Divisibility by 5 rule</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-6-rule.lesson>Divisibility by 6 rule</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-9-rule.lesson>Divisibility by 9 rule</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-10-rule.lesson>Divisibility by 10 rule</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-11-rule.lesson>Divisibility by 11 rule</A>, 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Restore-the-omitted-digit-in-a-number-in-a-way-the-number-is-divisible-by-9.lesson>Restore the omitted digit in a number in a way that the number is divisible by 9</A> &nbsp;and

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Restore-the-omitted-digit-in-a-number-in-a-way-the-number-is-divisible-by-11.lesson>Restore the omitted digit in a number in a way that the number is divisible by 11</A>.

in this site.