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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.

 Feb 4, 2022
 #1
avatar+69 
+4

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.

 

⚡⚡⚡

ShockFish

 Feb 4, 2022
edited by ShockFish  Feb 4, 2022
 #2
avatar+2440 
+1

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 \({22\over 90}= \color{brown}\boxed{11\over45}\)

 Feb 4, 2022

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