A contractor builds homes of 9 different models and presently has 4 lots to build on. In how many different ways can he arrange homes on these lots? Assume 4 different models will be built.
The answer is arrangements.
Answer
Final Answer: The contractor can arrange homes on these lots in \(\boxed{3024}\) different ways.
Step 1 ：We are given a problem where a contractor builds homes of 9 different models and presently has 4 lots to build on. We are asked to find out in how many different ways can he arrange homes on these lots, assuming 4 different models will be built.
Step 2 ：This is a permutation problem. The order in which the models are arranged matters, so we use the formula for permutations of n items taken r at a time, which is \(nPr = \frac{n!}{(n-r)!}\). Here, n is the total number of models (9) and r is the number of lots (4).
Step 3 ：Substituting the given values into the formula, we get \(9P4 = \frac{9!}{(9-4)!}\).
Step 4 ：Calculating the above expression, we find that the number of arrangements is 3024.
Step 5 ：Final Answer: The contractor can arrange homes on these lots in \(\boxed{3024}\) different ways.
