Artificial intelligence computer HAL \(9000\) randomly picks three distinct integers from between \(1\) and \(9000\)

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Artificial intelligence computer HAL \(9000\) randomly picks three distinct integers from between \(1\) and \(9000\) inclusive. If the first number picked is \(a,\) the second number picked is \(b,\) and the third number picked is \(c,\) what is the probability that \(a > b > c ?\)

A. \(\dfrac1{60}\)

B. \(\dfrac1{30}\)

C. \(\dfrac1{20}\)

D. \(\dfrac16\)

E. \(\dfrac13\)

Answer: D

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If you pick any three different numbers, there will be 3! = 6 different orders you can put them in. So if you pick three different numbers one at a time, the probability they will specifically be in decreasing order, one of the six possible orders, is 1/6.
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