9) How many possible calendars are there that have February 12 faliling on a Sun

Question

9) How many possible calendars are there that have February 12 faliling on a Sunday, Monday or Tuesday? Answer 9) 10) Your best friend is planning a trip to the Caribbean for you! You will visit Puerto Rico, St. Martin, the Dominican Republic, Belize, Jamaica, Cuba, and the U.S. Virgin Islands*. You can visit these islands in any order except that Cuba, Puerto Rico and the Dominican Republic must be visited one after the other on the itinerary. In how many ways can your friend arrange the itinerary? (# Assume that the US Virgin Islands is one destination.) Answer 10)

Explanation / Answer

total number of places to visit. =7

out of which 3 are to visit one after another. therefore we need to arrange 5 places/

hence total number of ways if (Cuba, Puerto Rico and Dominian Republic are not arranged within) =5! =120

Note:

total number of ways (if Cuba, Puerto Rico and Dominian Republic are to be arranged within) =5!*3! =120*6=720

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