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Considering the definition of permutation, in 95,040 different ways he can arrange homes on the lots.
<h3>Definition of Permutation</h3>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:
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
<h3>This case</h3>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:
Solving:
12P5= 479,001,600 ÷ 5,040
<u><em>12P5=95,040</em></u>
Finally, in 95,040 different ways he can arrange homes on the lots.
Learn more about permutation:
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