A number is a multiple of 8 if the last 3 digits of it, form a number which is a multiple of 8.
For example: 45288, 16840, 90024 are all multiples of 8, because 288, 840 and 024, the last 2 digits, are multiples of 8.
The total number of 8-digit numbers that we can form using {1,2,3,4,5,6} is
, as we have 6 options for each digit.
The last 3 digits of multiple of 8, formed from the set {1,2,3,4,5,6} can be one of the following:
{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} ,
which is 27 of them.
For each of these 3 digits fixed in the end, we can form
numbers
so in total, there are
numbers divisible by 8, whose digits are numbers in the set {1, 2, 3, 4, 5, 6}.
P(multiple of 8)=n(multiple of 8)/n(numbers that can be formed)=
Answer: 0.125
