The units digit of a three digit number is 6. What is the probability that the number is divisible by \(8\)? Express your answer as a common fraction.
+66 Let's organize our information.
_ _ 6
There are 9 * 10 ways to fill in the other two spots. (Because the first one can't be 0)
We check the first ones and we find that
136
216
256
works.
Each time the number grows by 40.
So this is (999 - 136) / 40 = 863 / 40 = 21.575, but then you have to count 136, thus the probability that the number is divisible by 8 is 22/90 = 11/45.
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ShockFish
+2668 There are \(9 \times 10\times 1 = 90\) options. There are \(22\) numbers that work: \(136,176,216,256,296,336,376,416,456,496,536,576,616,656,696,736,776,816,856,896,936,976\)
Thus... the answer is \({22\over 90}= \color{brown}\boxed{11\over45}\)
