Math Problem Statement
The scheduling supervisor at Wellington Medical Center must select four nurses from 16 who are available. How many different ways can that be done? Question content area bottom Part 1 The nurses can be selected enter your response here different ways. (Type a whole number.)
Solution
This is a problem of combinations since the order of selecting the nurses does not matter. To calculate the number of ways to select 4 nurses from a group of 16, we use the formula for combinations:
Where:
- is the total number of available nurses (16),
- is the number of nurses to be selected (4).
Substituting the values:
We can cancel out the terms from both the numerator and denominator, so:
Now, perform the multiplication and division:
Thus, there are 1820 different ways to select 4 nurses from 16.
Do you want more details or have any questions about the calculation?
Here are 5 related questions:
- How many ways can 5 nurses be selected from 20 nurses?
- What if the order of selection mattered? How would you calculate the number of arrangements (permutations)?
- How does the combination formula change if some selections are repeated?
- What is the difference between permutations and combinations?
- Can combinations be applied to different real-world scenarios like team formation?
Tip: When solving combination problems, remember that the order of selection doesn't matter. If order does matter, use the permutation formula instead.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Combinations
Formulas
Combination formula: C(n, r) = n! / (r!(n - r)!)
Theorems
Combination theorem
Suitable Grade Level
Grades 10-12
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