Respuesta :
Answer:
Option A
Step-by-step explanation:
In a train yard there are 6 flat cars, 7 box-cars and 3 livestock cars.
So total number of cars = 6 + 7 + 3
= 16
Now a train is to be made by 9 cars, out of 16 cars.
So number of ways the train can be made up will be =[tex]^{n}P_{r}[/tex]
where n = 16 and r = 9
so number of ways =[tex]^{16}P_{9}[/tex]
Option A is the answer.
Considering the definition of permutation, you use 16P9 to find the number of ways the train could be made up. (Option A).
What is 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.
That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.
In other words, permutations (or Permutations without repetition) 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:
[tex]mPn=\frac{m!}{(m-n)!}[/tex]
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 a train yard there are 6 flat cars, 7 box-cars and 3 livestock cars. So total number of cars is 6 + 7 + 3= 16.
A train is made up of 9 cars, out of 16 cars.
To obtain the total of ways in which 16 elements can be placed in 9 positions, you use the permutation 16P9.
Finally, you use 16P9 to find the number of ways the train could be made up. (Option A).
Learn more about permutation:
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