Respuesta :
First, let's state the given information:
The number of donors with the blood of type O+ is 6.
The number of donors with the blood of type A+ is 4.
The number of donors with the blood of type B+ is 2.
we will label these numbers as follows for reference:
[tex]\begin{gathered} a=6 \\ b=4 \\ c=2 \end{gathered}[/tex]We will also need the total number of donors "n":
[tex]\begin{gathered} n=6+4+2 \\ n=12 \end{gathered}[/tex]Since we are asked to find the distinguishable ways in which the donors can be in line, we need to find the number of permutations.
The formula for permutations is:
[tex]P=\frac{n!}{a!b!c!}[/tex]Where "!" means factorial, and is defined as follows, for example, 4! is:
[tex]4!=4\times3\times2\times1[/tex]And so on depending on the number.
In this case, the operation we have to solve is:
[tex]P=\frac{12!}{6!4!2!}[/tex]Solving this division we get the result for the number of distinguishable ways in which the donors can be in line:
[tex]P=13,860[/tex]Answer: 13,860
