+2440 About every two years, usually during an odd year, some idiot posts a simple expression with a wrong answer for its simplification and resolution to a numerical result. The same idiot also claims the calculator does not solve it correctly because it fails to follow the order of operations [PEMDAS or BIDMAS] correctly.
This year, you are the idiot!
The expression, as presented, equals (25) not one (1).
If by “distribution rules” you mean Arithmetic Order of Operation Hierarchy, then this calculator follows all (except for one*) of them, including the exceptions for variables usage, where Implicit multiplication of variables takes precedents over division – a formally adopted exception, dating back to the 1968 mathematical society convention that included updates on mathematical order of operations hierarchy.
As for your brain-dead expression, the calculator correctly resolves this to (25).
20/4(3+2) = 25 | This is correct for Arithmetic Order of Operation Hierarchy
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Note: by using a variable, then this resolves to one (1). This makes use of the exceptions for implicitly multiplied variables before division (described above).
x=4; 20/(x)(3+2) = 1 Though the parenthetical operation of (3+2) is not a variable it’s treated as one because of the variable preceding it and the implicit multiplication.
Also, by placing parenthesis around the (4), the calculator will use the variable-exception rule.
20/(4)(3+2) = 1 Again, note that multiplication is implied between the parenthetical operations.
[It’s also notable that when math is resolved or solved electronically, parenthetical operations are treated as variables in the registers.]
If the multiplication is made explicit with a * then:
20/(4)*(3+2) = 25 ... the operations revert back to standard PEMDAS.
This matches the answer you claim is correct, but ...
Your expression does not have a variable, so the exception for implicitly multiplied variables before division does not apply. This calculator is smarter than you are!
Additional notes:
*This calculator’s exception for Arithmetic Order of Operation Hierarchy occurs for the Stacked Power convention:
Formal operation: Stacked powers (aka: Power Towers) are (exponentially) multiplied from the right to left (from the top down), and the resultant product becomes the EXPONENT to the base number.
For this calculator, the Arithmetic Order of Operation Hierarchy is not followed for Stacked Powers. The web2.0calc calculator resolves this from the left to right or ascending order, where the resultant product becomes the BASE of the next exponent. This operation is clearly defined in the interpretation space, above the calculator.
Generally, power-towers are used in advanced, theoretical mathematics. For the majority of occasions where the construction of a power-tower occurs in an equation for the physical sciences, the ascending method is almost always used for its resolution (the descending method is rarely used). This is probably why Herr Mossow elected to code the calculator with the ascending method as the default operation. This calculator, which is actually a computational engine, is orientated toward the physical sciences, which is why it’s referenced as a Scientific Calculator.
Related post: https://web2.0calc.com/questions/8-2-2-2
GA
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+2440
Solution:
Remove slop solution ... replace with a correct solution.
Case analysis of binomial distribution.
\(\huge \rho(x) \normalsize = \dfrac { \left [\dbinom {7}{1} \dbinom {4}{3} \right] * \left[ \left (\dbinom {6}{2} \dbinom {4}{1}\dbinom {4}{1} \right ) + \left(\dbinom {6}{1} \dbinom {4}{2}\right) \right]} {\dbinom {28}{5}} = \underbrace {\left (\large \dfrac {46}{585}\right)}_{\text {exact probability}} \left ( \approx 7.86\% \right )\\ \)
Expansion, Dissection, and Description:
nCr(7,1)*nCr(4, 3) * nCr(6,2)*nCr(4, 1)*nCr(4, 1) = 6720 |Counts of triples with non-pairs.
Choose one (1) of seven (7) numbers; choose three (3) of the four (4) colors; choose two (2) of the six (6) remaining numbers; choose one (1) of four colors for each of the two (2) numbers.
nCr(7,1)*nCr(4, 3) * (nCr(6,1)*nCr(4, 2) = 1008 |Counts of triples and only pairs.
Choose one (1) of seven (7) numbers; choose three (3) of the four (4) colors; choose one (1) of the six (6) remaining numbers; choose two (2) of the four (4) colors –making a pair of numbers.
Add these counts: 6720 + 1008 = 7728
Divide: 7728/ nCr(28,5) = 46/585 = 7.86%
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See also Tiggsy's solutions
GA
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