Question 188328
<font face="Goudy Old Style" size="+2">


Let <i>p</i> = the probability that all the pieces are white.  Since your problem statement makes absolutely no mention of the colors of the pieces or the distribution of colors on the pieces, it is equally likely that all of the pieces are white as it is that none of the pieces are white as it is that any other number of pieces are white between those two limits.  Therefore, all that can be said is that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  0 \leq p \leq 1]


Where:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ p = \frac{n_w}{42},\ n_w\,\in\,\I,\ 0 \leq n \leq 42]


*[tex \Large n_w] being the number of white pieces.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>