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Chapter 5: Problem 44

An environmental agency will randomly select 4 houses from a block containing 25 houses for a radon check. How many total selections are possible? How many permutations are possible?

Short Answer

Expert verified
The total number of combinations (selections) and permutations will be calculated using the formulas in step 2 and step 3 respectively.

Step by step solution

01

Define the Problem Variables

Total number of houses, \(n\), is 25. The number of houses selected, \(r\), is 4.
02

Calculate the Combinations

Combinations can be calculated using the formula \(C(n, r) = n! / [r!(n-r)!]\), where '!' denotes the factorial operation. Substituting \(n = 25\) and \(r = 4\) in the formula, we find the total number of possible combinations or selections.
03

Calculate and Permutations

Permutations can be calculated using the formula \(P(n, r) = n! / (n-r)!\). Substituting \(n = 25\) and \(r = 4\) in the formula, we find the total number of possible permutations.
04

Final Step - Results Interpretation

After calculating in steps 2 and 3, the results are interpreted. The total number of combinations or selections is the total number of ways 4 houses can be selected from 25. The total number of permutations is the total number of ways these 4 houses can be arranged.

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