Timothy's 9-digit Dilemma

Discrete Mathematics Level 3

Timothy had finished writing all 9-digit numbers that contains numbers (1-9) and without repeating the same digit in the same number, and he was rather pleased with himself.

'There all 362880 numbers, and it took me just 2 days!', he boasted to his friend.

'Why would you torment yourself like that?', ask the very confused friend.

'It's factorial fun!' came the reply

At that very moment, the enthusiastic maths teacher suddenly appeared! 'Aha! I see what you have there! When I was your age I did the exactly same thing! But do you know how many of these numbers are divisible by 6?'

The friend, feeling very awkward, decide to fade away into the background.

'Well... I know that all numbers divisible by 6 are divisible by 2 AND 3; but would I need to divide every individual number with 6 over and over?', stated Timothy feeling glum.

The teacher replied, ' Oh no, you do not need to, Just figure out what has to be done; I know you learnt factorials.'

Timothy managed to find the right answer, and his teacher commended him. What was Timothy's answer?


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