## 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 $$9000$$

by VJesus12 » Fri Jun 11, 2021 8:09 am

00:00

A

B

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D

E

## Global Stats

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. $$\dfrac13$$

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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