+1 vote
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Question: Six different airlines fly from New York to Denver and seven fly from Denver to San Francisco. How many different pairs of airlines can you choose on which to book a trip from New York to San Francisco via Denver, when you pick an airline for the flight to Denver and an airline for the continuation flight to San Francisco ? How many of these pairs involve more than one airline ?

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+1 vote

I think they are asking for the following thing:

N.Y to Denver available flights                   Denver to San Francisco available flights

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x1, x2, x3, x4, x5, x6​​​​​,                                         x1, x2, x3, x4, x5, x6​​​​​, x7

I have choosen the same airlines for Denver to San Francisco because of the last question.

Now, different ways in which you can reach from N.Y to San Francisco

= 6 * 7

= 42

Now, to find answer to last question, we apply inclusion -exclusion.

= total ways    -     #ways in which the flight taken from N.Y to Denver

is also continued from Denver to San Francisco

= 42 - 6

= 36

But how can we assume that  Denver to San Francisco has same 6 flights as from N.Y to Denver?
Because of the last question

+1 vote