Question 978719
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.