<s>[INST] Probability two blocks have exactly 2 out of 4 properties the same? 
I have 120 blocks. Each block is one of 2 different materials, 3 different colors, 4 different sizes, and 5 different shapes. No two blocks have exactly the same of all four properties. I take two blocks at random. What is the probability the two blocks have exactly two of these four properties the same?

I ended up getting:
$${{\binom{2}{1}\binom{3}{1}\binom{4}{2}\binom{5}{2} + \binom{2}{1}\binom{3}{2}\binom{4}{1}\binom{5}{2} + \binom{2}{1}\binom{3}{2}\binom{4}{2}\binom{5}{1} + \binom{2}{2}\binom{3}{1}\binom{4}{1}\binom{5}{2} + \binom{2}{2}\binom{3}{1}\binom{4}{2}\binom{5}{1} + \binom{2}{2}\binom{3}{2}\binom{4}{1}\binom{5}{1}}\over{\binom{120}{2}}} = {{41}\over{238}}$$Is this correct?
EDIT: The answer given here is ${{35}\over{119}} = {5\over{17}}$:
https://web2.0calc.com/questions/probability-question-blocks
Who is correct?
 [/INST] You have made a simple arithmetic error. I evaluated your expression and I got $\dfrac{5}{17}$.
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