the movies...again! That\'s right, they haven\'t defriended The Scooby Doo gang
ID: 3147115 • Letter: T
Question
the movies...again! That's right, they haven't defriended The Scooby Doo gang is going to Fred in real life (yet). Enter your answers for this problem as integers Suppose a row of seats at the movies is 11 seats, and that this row will be filled up completely by the 5 members of the Scooby Doo gang, and 6 strangers. How many arrangements of these 11 people are possible, such that the Scooby Doo gang can all sit adjacent to one another in this row? Now suppose Fred is being a huge jerk, so the Scooby Doo gang decides he has to sit on one of the ends of their group of 5 (not necessarily an end of the row). How many possible arrangements of the 11 people in the row are there now? Sanity check: Should your answer for this part be greater than or less than the answer from the first part?Explanation / Answer
First part: Since all 5 members of Scooby Doo gang sit together, let us take the gang as one person.
There are 1 + 6 = 7 persons and they can be arranged in 7! = 5040 ways.
Further, the members of the gang can sit in 5! = 120 ways.
=> Total number of seatings = 5040 * 120 = 604800.
Second part: Since Fred sits at one of the ends, the remaining four form a 'small' person. The gang itself is taken as a person and so the 7 persons can as earlier be seated in 7! = 5040 ways.
Within the gang however, Fred has 2 choices and the remaining 4 people can sit in 4! = 24 ways. The gang therefore can sit in 2 * 24 = 48 ways.
=> Total number of seatings = 5040 * 48 = 241920.
Sanity check: Naturally the second part should have a smaller number as the result as there are more seating restrictions.
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