Question

contractor wishes to build 9 houses, each different in design. In how many ways can he place these houses on a street if 6 lots are on one side of the street and 3 lots are on the opposite side?

Answer 1

The houses can be placed in 362,880 ways.

Explanation:

The 9 houses are each in different design.

The each lot can place any of the 9 houses.

• The 1st lot can place anyone house of all the 9 houses.
• The 2nd lot can place one of remaining 8 houses.
• The 3rd lot can place one of remaining 7 houses.

Similarly, the process gets repeated until the last house is placed on a lot.

From the above steps, it can be determined that :

The number of ways to place the 9 houses in 9 lots = 9!

⇒ 9×8×7×6×5×4×3×2×1

⇒ 362880 ways.

Therefore, the houses can be placed in 362880 ways.