**Permutations of Donors with Different Blood Types**At a blood drive, there are 5 donors with type O+ blood, 5 donors with type A+ blood, and 2 donors with type B+ blood queued up. We need to determine in how many distinguishable ways these donors can be arranged in line.To solve this problem, we use the formula for permutations of a multiset:\[ \frac{n!}{n_1! \cdot n_2! \cdot n_3!} \]Where:- \( n \) is the total number of items,- \( n_1 \), \( n_2 \), and \( n_3 \) are the counts of each distinct type of item.Given data:- Total number of donors (\( n \)) = 5 (O+) + 5 (A+) + 2 (B+) = 12.- \( n_1 \) (O+ donors) = 5.- \( n_2 \) (A+ donors) = 5.- \( n_3 \) (B+ donors) = 2.Thus, the number of distinguishable ways the donors can be arranged in line is calculated as:\[ \frac{12!}{5! \cdot 5! \cdot 2!} \]Place the computed number in the following box:The donors can be in line in \[ \boxed{} \] different ways.

Solution-: Given: Number of donors with type O+ =5 Number of donors with type A+ =5…

At a blood drive, 5 donors with type O + blood, 5 donors with type A + blood, and 2 donors with type B + blood are in line. In how many distinguishable ways can the donors be in line? The donors can be in line in different ways. ...

At a blood drive, 5 donors with type O + blood, 5 donors with type A + blood, and 2 donors with type B + blood are in line. In how many distinguishable ways can the donors be in line? The donors can be in line in different ways. ...

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.1: Counting

Problem 1E: The Fundamental Counting Principle says that if one event can occur in m ways and a second event can...

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Question

**Permutations of Donors with Different Blood Types**

At a blood drive, there are 5 donors with type O+ blood, 5 donors with type A+ blood, and 2 donors with type B+ blood queued up. We need to determine in how many distinguishable ways these donors can be arranged in line.

To solve this problem, we use the formula for permutations of a multiset:

\[ \frac{n!}{n_1! \cdot n_2! \cdot n_3!} \]

Where:
- \( n \) is the total number of items,
- \( n_1 \), \( n_2 \), and \( n_3 \) are the counts of each distinct type of item.

Given data:
- Total number of donors (\( n \)) = 5 (O+) + 5 (A+) + 2 (B+) = 12.
- \( n_1 \) (O+ donors) = 5.
- \( n_2 \) (A+ donors) = 5.
- \( n_3 \) (B+ donors) = 2.

Thus, the number of distinguishable ways the donors can be arranged in line is calculated as:

\[ \frac{12!}{5! \cdot 5! \cdot 2!} \]

Place the computed number in the following box:

The donors can be in line in \[ \boxed{} \] different ways.

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