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if we have $p$ variables, the number of scatter plots we have is :

$p(p-1)/2$.

Why is this so? Is there any one who can explain this formula?

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When you have p variables and would like to have scatter plots for 2 variables each then number of combinations come upto p combination 2(Pc2 # P subscript C subscript 2) by expanding the formula you get p(p-1)/2

sorry i don't know to add subscripts here so i wrote subscript

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When you represent all the scatter plots, you only want to plot the pairs of different variables. And:

$$\binom{p}{2}=\frac{p(p-1)}2$$

As @NickCox stressed, the plot of $y$ versus $x$ contains the same points as that of $x$ versus $y$ (up to exchange of axes).

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