Considering the definition of permutation, in 95,040 different ways he can arrange homes on the lots.
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:
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.
In this case, you know:
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= 12!÷ (12-5)!
Solving:
12P5= 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:
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