A young upstart tries to drum up business in three of the ta

A young upstart tries to drum up business in three of the tallest buildings in the city: One World Trade Center (104 floors), the Empire State Building (86 occupied floors) and the Bank of America Tower (55 floors). In one week, the businessman was on floor 12, 15, 18, 32 and 59. What is the probability he visited One World Trade Center for more than one of those days?

I\'ve noticed that the Bank of America Tower only has 55 floors, so I\'m guessing that\'s something to take into consideration...

Solution

Total number of ways he can drum up business in the three buildings = 3C1 * 3C1 * 3C1 * 3C1 * 2C1

                                                                                                               = 162

Number of ways he had visited One World Trade Center for one day = 4C1 * 1 * 2C1 * 2C1 * 2C1 * 1 + 2C1 * 2C1 * 2C1 * 2C1 * 1 = 32 + 16 = 48

probability = 1 - 48 /162 = 0.7037