Question

A nine digit number is written using 1,2,3,4 5,6,7,8,9 without repetition find the probability that number is divisible by 9

Answer 1

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

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Answer 2

Total outcomes:3 & 9

Therefore, p(no. Divisible by 9)

=2 by 9