SOLUTION: if 7 houses of different designs are to be constructed in a housing project so that 4 particular designs are to be constructed on one side of a street and the remaining 3 on the ot
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Question 978719: if 7 houses of different designs are to be constructed in a housing project so that 4 particular designs are to be constructed on one side of a street and the remaining 3 on the other side, in how many ways can the houses be placed? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the 4 houses on one side of the street can be placed in 4! ways where each arrangement is different from the other arrangement and no design is used more than once.
4! = 4*3*2*1 = 24 possible arrangements on one side of the street.
similarly on the other side of the street, the 3 houses can be placed in 3! ways where arrangement is different from the other arrangement and no design is used more than once.
3! = 3*2*1 = 6 possible arrangements.
the total number of possible arrangements is 24 * 3 = 72 possible arrangements.
