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AMC 10 2013 A #17

 
 
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Re: AMC 10 2013 A #17
LensmireJohn - 2021年10月11日 Monday 11:16
 

The overlaps are a little complicated here and we have to be careful with our overcounting in this case. Your numbers are all correct, but let's look at them a little more carefully:

  1. 30 days where A and B visit
  2. 24 days where A and C visit
  3. 18 days where B and C visit
  4. 6 days where A, B, and C visit

We want to count the number of days where exactly 2 of the 3 visit, so we start with 30+24+18, but this is overcounting.

For the overcounting, note that if A, B, and C visit all visit (situation #4 above), that is also counted in situations #1, #2, and #3. Thus, situation #4 is overcounting 6 times when we're counting situation #1, but also 6 times in situation #2 and #3.

Hence, we actually need to subtract 3*6 = 18 from 30+24+18 to get a final answer of 54. Hope this helps!