carlos.lara.7 wrote:After a business trip to London, Michele has enough time to visit three European cities before returning home. If she has narrowed her list to six cities that she'd like to visit - Paris, Barcelona, Rome, Munich, Oslo, and Stockholm - but does not want to visit both Oslo and Stockholm on the same trip, how many different sequences of three cities does she have to choose from?
a)36
b)48
c)72
d)96
e)120
Good arrangements = all possible arrangements - bad arrangements.
All possible arrangements:
Number of options for the first visited city =
6. (Any of the 6 cities.)
Number of options for the second visited city =
5. (Any of the 5 remaining cities.)
Number of options for the third visited city =
4. (Any of the 4 remaining cities.)
To combine the options in blue, we multiply:
6*5*4 = 120.
Bad arrangements:
A bad arrangement includes both Oslo and Stockholm.
Number of options for the third city to be combined with Oslo and Stockholm =
4. (Any of the 4 other cities.)
Number of ways to arrange the 3 cities = 3! =
6.
To combine the options in blue, we multiply:
4*6 = 24.
Good arrangements:
All possible arrangements - bad arrangements = 120-24 = 96.
The correct answer is
D.
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