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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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Answer. This probability is equal to 1.
Solution
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.
On 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.