Question

A contractor builds homes of 12 different models and presently has 5 lots to build on. In how many different ways can he arrange homes on these lots? Assume 5 different models will be built.

Answer 1

Considering the definition of permutation, in 95,040 different ways he can arrange homes on the lots.

Definition of Permutation

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.

In other words, permutations are ways of grouping elements of a set in which:

• take all the elements of a set.
• the elements of the set are not repeated.
• order matters.

To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:

$m Pn=\frac{m!}{(m-n)!}$

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

This case

In this case, you know:

• A contractor builds homes of 12 different models.
• Presently the constractor has 5 lots to build on.

To obtain the total of ways in which he can arrange homes on these lots, you use the permutation. This is, 12 elements o models can be arranged occupying only the 5 positions:

$12P5=\frac{12!}{(12-5)!}$

Solving:

$12P5=\frac{12!}{7!}$

12P5= 479,001,600 ÷ 5,040

12P5=95,040

Finally, in 95,040 different ways he can arrange homes on the lots.

Learn more about permutation:

brainly.com/question/12468032

brainly.com/question/4199259

#SPJ4