First time here? Checkout the FAQ!
+1 vote

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 ?


asked in Combinatory by (287 points)  
edited by | 187 views

1 Answer

+1 vote

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.


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

                             is also continued from Denver to San Francisco

= 42 - 6

= 36


answered by Veteran (15k points)  
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

Top Users May 2017
  1. akash.dinkar12

    3154 Points

  2. pawan kumarln

    1630 Points

  3. sh!va

    1590 Points

  4. Arjun

    1350 Points

  5. Devshree Dubey

    1246 Points

  6. Angkit

    1044 Points

  7. Debashish Deka

    1022 Points

  8. Bikram

    972 Points

  9. LeenSharma

    836 Points

  10. Prashant.

    692 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 22 - 28
  1. pawan kumarln

    256 Points

  2. Ahwan

    236 Points

  3. jjayantamahata

    114 Points

  4. joshi_nitish

    114 Points

  5. Arnab Bhadra

    94 Points

22,731 questions
29,061 answers
27,627 users