How many travel options

Question

Amber wants to visit Dallas,Philadelphia, El Paso,LA,Phoenix,Jacksonville,San Diego,Memphis,San Jose, Houston and Boston. If she decides to visit some,all or none of these cities how many travel options does she have

 

Answer 1

To understand this problem, you must understand the phrase, "visit some, all or none of these cities."

 

The best way to view the travel options is from the view of the cities, not from the view of the traveler.  Each city may be visited ort not -- that's the option!!

 

Given 11 cities, there are 2*2*2*2*2*2*2*2*2*2 (that is, 2¹¹) possibilities. And, 2¹¹ = 2048.

 

Now, if you want to learn the binary (base 2) number system, you may count:

  D   P  EP  LA  P   J  SD  M SJ  H   B

  0   0   0   0   0   0   0   0   0   0   0        [visit none; 0000]

  0   0   0   0   0   0   0   0   0   0   1     [visit some]

  0   0   0   0   0   0   0   0   0   1   0

  0   0   0   0   0   0   0   0   0   1   1

  0   0   0   0   0   0   0   0   1   0   0

  . . . . . . . . . . . . . . . . . . . . . . . . .

  1   1   1   1   1   1   1   1   1   1   0

  1   1   1   1   1   1   1   1   1   1   1       [visit all; 2047]