Artificial intelligence computer HAL $9000$ randomly picks three distinct integers from between $1$ and $9000$

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

Source: GMAT Club Tests

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Re: Artificial intelligence computer HAL $9000$ randomly picks three distinct integers from between $1$ and $9000$

by Ian Stewart » Sat Jun 12, 2021 4:26 pm

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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