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On page 383, section 10.2. of the Algorithms for Planning as State Space Search chapter of the textbook Artificial Intelligence: A Modern Approach, the following passage appears:

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In this passage, the authors write that in the air cargo example they use there are $50^{10} \times 200^{50+10} \approx 10^{155}$ states.

Is this incorrect? Shouldn't there be $10^{50} \times 60^{200}$ states?

As far as my understanding of probability goes, there is a different state for all the different arrangements of the 50 planes, which can each be at one of 10 airports, which would give the result $10 \times 10 \times ... = 10^{50}$, and then the same reasoning applied to the placement of the packages on an airplane or at an airport gives $60 \times 60 \times ... = 60^{200}$, which together give $10^{50} \times 60^{200}$.

Is the textbook incorrect or is my reasoning incorrect?

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Yes. You are right. That looks like an error in the textbook. Check their errata, or send the authors a note to let them know.

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  • $\begingroup$ There used to be a Google Drive document linked from the errata form, which had many more errors than the errata page. But it's no longer there. $\endgroup$ – David Richerby Mar 29 '18 at 22:39
  • $\begingroup$ I just sent the authors a note. Thanks for the suggestion. $\endgroup$ – Sun T Mar 29 '18 at 23:18

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