Kenneth Rosen Edition 6th Exercise 5.1 Question 5 (Page No. 344)

Question

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 ?

Answer 1

I think they are asking for the following thing:

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

-------------------------------------------------------------------

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.

Answer

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

                             is also continued from Denver to San Francisco

= 42 - 6

= 36

Comments

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