specific probability

Question

A certain internet cafe assigns a 4 character log in (At random)

These Characters are composed of all the letters of the alphabet including upper case and lower case plus 0-9.

So if i am counting this right , there are 62 different possible characters... out of a 4 characters, "log in", what are the odds of 3 out of 4 being 828... And in this order...

This actually happened to me recently... I have used this internet cafe 1000s of times and i never got even 2 numbers in a row before let alone 3 !

the numbers 828 have a specific meaning for me, at this point in my life, that almost no one knows except me...

So what are the odds of this happening?

Answer 1

The probability will be the number of ways 828 comes up in order divided by the total possible login pwds.

There are 62 ways to get one 828 and the 828 can be in 2 positions - 124 ways If you allow the 828 to be separated and in the same order, there are 4 positions)

The total possible is 62⁴

About 8 x 10^-6