Tonya's ZIP code is 24760. How many zip codes altogether could be formed, each one using those same five digits? zip codes (Type a whole number.) ...
Tonya's ZIP code is 24760. How many zip codes altogether could be formed, each one using those same five digits? zip codes (Type a whole number.) ...
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Interactive Exercise: Permutations of ZIP Codes**
**Problem Statement:**
Tonya's ZIP code is 24760. How many unique ZIP codes can be created by rearranging these five digits?
**Input Box:**
[ ] zip codes
(Type a whole number.)
**Instruction:**
Calculate the total number of unique permutations of the digits in the given ZIP code. Use the concept of factorial to determine how many different ways the digits 2, 4, 7, 6, and 0 can be arranged.
**Educational Note:**
To solve the problem, find the factorial of the number of digits. Since there are 5 unique digits, calculate \(5!\) (5 factorial), which is:
\[5! = 5 \times 4 \times 3 \times 2 \times 1\]
**Expected Answer Format:**
Provide your answer as a whole number reflecting the total number of possible permutations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F038c6036-1a7a-4532-92c2-f9b6fb00a9e2%2F6de25f71-667f-4875-976c-3b21de7e9260%2Fezobro_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Interactive Exercise: Permutations of ZIP Codes**
**Problem Statement:**
Tonya's ZIP code is 24760. How many unique ZIP codes can be created by rearranging these five digits?
**Input Box:**
[ ] zip codes
(Type a whole number.)
**Instruction:**
Calculate the total number of unique permutations of the digits in the given ZIP code. Use the concept of factorial to determine how many different ways the digits 2, 4, 7, 6, and 0 can be arranged.
**Educational Note:**
To solve the problem, find the factorial of the number of digits. Since there are 5 unique digits, calculate \(5!\) (5 factorial), which is:
\[5! = 5 \times 4 \times 3 \times 2 \times 1\]
**Expected Answer Format:**
Provide your answer as a whole number reflecting the total number of possible permutations.
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