Amber wants to visit Houston Indianapolis Philadelphia Fort

Amber wants to visit Houston, Indianapolis, Philadelphia, Fort Worth, Seattle, Columbus, Boston, Los Angeles, Memphis, and Jacksonville. If she decides to visit some, all, or none of these cities, how many travel options does she have? She has travel options. (Simplify your answer.)

Solution

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Given 10 cities and Amber wants to visit some, none or all of these cities

ie. .

If Amber decides to visit 0 cities no of ways = 10C0

1 city = 10C1

2 Cities = 10C2

.

.

10Cities = 10C10

Total Number of ways = 10C0 + 10C1 + 10C2 + ........ + 10C9 + 10C10

= 2^10 (As we know that nC0 + nC1 + ... + nCn ) = 2^n

=1024 ways Solution