8. When a student multiplied the number 66 by the repeating decimal 1.abab... = 1.ab.
where a and b are digits, he did not notice the notation and just multiplied
66 times 1.ab. Later he found that his answer is 0.5 less than the correct
answer. What is the 2-digit integer a b?
(A) 15
(B) 30 (C) 45 (D) 60 (E) 75

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.

whaere is the picture

step-by-step explanation:

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."