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Two different numbers are selected simultaneously and at random from the set {1,2,3,4,5,6,7}. What is the probability that the positive difference between the two numbers is 3 or greater? Express your answer as a common fraction.

 Jul 31, 2022
 #1
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There are \({7 \choose 2} = 21 \) choices

 

The only cases that work are (1, 4), (1, 5), (1, 6), (1, 7), (2, 5), (2, 6), (2, 7), (3, 6), (3, 7), (4, 7)

 

So, the probability is \({9 \over 21} = \color{brown}\boxed{3 \over 7}\)

 Jul 31, 2022
 #2
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BuilderBoi: You missed the count by 1. Should read: 10 / 21

Guest Aug 1, 2022
 #3
avatar+2448 
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Yep, you're right... 

 

I listed 10 cases but put the probability as 9/21.

BuilderBoi  Aug 2, 2022

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