9. A personal identification number (PIN) that opens a certain lock consists of a sequence of 3 different digits from 0 through 9, inclusive. How many possible PINS om thoro?
9. A personal identification number (PIN) that opens a certain lock consists of a sequence of 3 different digits from 0 through 9, inclusive. How many possible PINS om thoro?
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![**Question 9:** A personal identification number (PIN) that opens a certain lock consists of a sequence of 3 different digits from 0 through 9, inclusive. How many possible PINs are there?
**Explanation:**
To solve this problem, we need to determine how many different sequences of three digits we can create from the digits 0 through 9, with each digit being used only once in each sequence.
1. **Choose the first digit:** There are 10 possible digits (0-9).
2. **Choose the second digit:** Since each digit must be different, there are 9 remaining choices after selecting the first digit.
3. **Choose the third digit:** After selecting the first and second digits, there are 8 remaining choices.
The total number of different PINs is calculated by multiplying these choices together:
\[ 10 \times 9 \times 8 = 720 \]
Therefore, there are 720 possible different PINs that can be formed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71fa1030-1346-4e6e-92c7-d0e537b79d38%2F71da91b4-a822-411d-ae69-94d722cdf55e%2Fkzkv4dc_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 9:** A personal identification number (PIN) that opens a certain lock consists of a sequence of 3 different digits from 0 through 9, inclusive. How many possible PINs are there?
**Explanation:**
To solve this problem, we need to determine how many different sequences of three digits we can create from the digits 0 through 9, with each digit being used only once in each sequence.
1. **Choose the first digit:** There are 10 possible digits (0-9).
2. **Choose the second digit:** Since each digit must be different, there are 9 remaining choices after selecting the first digit.
3. **Choose the third digit:** After selecting the first and second digits, there are 8 remaining choices.
The total number of different PINs is calculated by multiplying these choices together:
\[ 10 \times 9 \times 8 = 720 \]
Therefore, there are 720 possible different PINs that can be formed.
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