No repeat digits

A company uses 2-factor logins for its computers. Each employee has a small digital device that generates a random 6-digit number every minute.

What is the probability that a given number has no repeated digits?

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@AThousandYoung

Correct.

The way I did it was:

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What are the odds that each number will be equal to or less than the previous number?

@athousandyoung said
What are the odds that each number will be equal to or less than the previous number?

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@bigdogg said
[hidden]0.5005%[/hidden]

@bigdogg said
I never did find a formula for this. There probably is one, if you're 'mathy' enough.

I asked a 'mathy' person about this. Turns out there is a formula.

The sequence can be thought of as a combination of six digits and 9 markers. The markers reduce the digit value by 1.

For example, the number 998877 is shown as:
99-88-77-------

And the number 997777 is shown as:
99--7777-------

As Joe Shmo tried to teach us, before he got banned, the way of calculating the number of 6-digit possibilities spread out over 15 total positions is:

n! / [ k! * (n-k)! ]
15! / [6! * (15-6)! ]
= 15! / [6! * 9! ]
= 15*14*13*12*11*10 / 6*5*4*3*2*1
= 3603600 / 720
= 5005

5005 out of 1 million numbers is a probability of 0.5005%, which matches what I got from my program.

@bigdogg said
I asked a 'mathy' person about this. Turns out there is a formula.

The sequence can be thought of as a combination of six digits and 9 markers. The markers reduce the digit value by 1.

For example, the number 998877 is shown as:
99-88-77-------

And the number 997777 is shown as:
99--7777-------

As Joe Shmo tried to teach us, before he got banned, the way of calc ...[text shortened]... 5005 out of 1 million numbers is a probability of 0.5005%, which matches what I got from my program.

@venda said
Thanks for that.Just the sort of thing I like
I'll keep the formula for future reference.
I didn't know Joe was banned.
What was that all about?

@bigdogg said
He kept posting alt-right links in Debates after he was told to desist.

Hence the smattering of posts by "Removed" in this forum's history.