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At a blood drive, 6 donors with type O + blood, 4 donors with type A + blood, and 2 donors with type B + blood are in line. In how many distinguishable ways can thedonors be in line?The donors can be in line in different ways.2

User Kieran Hunt
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1 Answer

7 votes
7 votes

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:


\begin{gathered} a=6 \\ b=4 \\ c=2 \end{gathered}

We will also need the total number of donors "n":


\begin{gathered} n=6+4+2 \\ n=12 \end{gathered}

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:


P=(n!)/(a!b!c!)

Where "!" means factorial, and is defined as follows, for example, 4! is:


4!=4*3*2*1

And so on depending on the number.

In this case, the operation we have to solve is:


P=(12!)/(6!4!2!)

Solving this division we get the result for the number of distinguishable ways in which the donors can be in line:


P=13,860

Answer: 13,860

User Kimses
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