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Dakota randomly selected three different integers 1 through 6 What is the probability that the three numbers selected could be the sides of a right triangle?

 Jan 21, 2021
 #1
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+1

3 4 5 triangle is the only one I am aware

 

6 c 3 = 20   choices for 3 sides

 

1 choice   3 4 5   works       1/20  or  5%

 Jan 21, 2021
 #2
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+2

this case is the range of numbers choose sides of a triangle. 

 

so 6 choose 3 = 20

 

and we want to choose a set of numbers that when you apply the pythagorean theorem (a^2+b^2+c^2) the result is a whole number

 

only 3, 4, and 5 works in this case between the range 1 to 6 (proof: 3^2+4^2=9+16=25, 25=5^2)

 

so 1, 2, and 6 doesn't work

 

so the probablility is 1/2 if no number can be used more than once. 

 

but if a number can be used more than once in the range 1 to 6 (still only the set 3, 4, and 5 works), then the answer is 1/6 choose 3 = 1/20

 Jan 21, 2021
edited by KitSoundwave  Jan 21, 2021
edited by KitSoundwave  Jan 21, 2021

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