Posted by **Anonymous** on Friday, July 27, 2012 at 5:47pm.

A fair, six-sided die is rolled eight times, to form an eight-digit number. What is the probability that the resulting number is a multiple of 8? Express your answer as a common fraction.

- math -
**Reiny**, Friday, July 27, 2012 at 9:56pm
Total number of numbers using 1-6

= 6^8 = 1679616

For any number to be divisible by 8, its last 3 digits must be divisible by 8

but these last two digits must contain only the digits from 1 to 6, with no zeros.

possible cases are:

112 136 144 152

216 224 232 256 264

312 336 344 352

416 424 432 456 464

512 536 544 552

616 624 632 656 664

Hoping that I didn't miss any, I count 27

so the front 5 numbers could be anything

there are 6^5 or 7776 different front numbers, each of those could have 27 different last three numbers

so there are 7776x27 or 209952 which are divisible by 8

prob that a number is a multiple of 8

= 209952/1679616

26244/209952

= 6561/52488

= 1/8

mmmmh, very interesting

- math -
**yes**, Monday, July 29, 2013 at 6:56am
That is right

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