(Sheldon Ross, Probability, 7.11.)
What is the expected number of married couples sitting together?
The solution is this image, and I do not understand the final summation. How are there 22 & 19 different women?
2026-04-13 19:26:38.1776108398
20 people, (10 married couples) are to be seated at 7 tables, 3 tables contain 4 seats, 4 tables contain 2 seats.
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I don't understand it either. Once I was at the next to last line I would just say $\sum_{j=1}^7X_{i,j}=3\cdot \frac 3{95}+4\cdot \frac 1{190}=\frac {11}{95}$ and the $i$ sum doesn't depend on $i$, so $E[X]=10 \cdot \frac {11}{95}=\frac {22}{19}$