23. On a balance scale, three different masses were put at random on each pan and the result is shown in the picture. The masses are of 101,102 , $103,104,105$ and 106 grams. What is the probability that the 106 gram mass stands on the heavier pan?
A $75 \%$
B $80 \%$
C $90 \%$
D $95 \%$
E $100 \%$
23. B The total mass is $621 \mathrm{~g}$ so any three masses with total mass over $310.5 \mathrm{~g}$ could be in the heavier pan. There are eight of these triples that include the $106 \mathrm{~g}$ mass: $(106,105,104)$, $(106,105,103),(106,105,102),(106,105,101),(106,104,103),(106,104,102),(106$, $104,101)$, and $(106,103,102)$.
Without 106 , there are 2 ways to make a set over $310.5 \mathrm{~g}$ : $(105,104,103)$ and $(105,104$, 102 ).
Hence the probabililty that the $106 \mathrm{~g}$ mass is included in the heavier pan is $\frac{8}{8+2}=\frac{8}{10}$ or $80 \%$.