Math Problem Statement
A small combination lock on a suitcase has 5 wheels, each labeled with the 10 digits 0 to 9. How many 5 digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different? Question content area bottom Part 1 a. The number of different 5 digit combinations possible if no digit is repeated is 30,240 . Part 2 b. The number of different 5 digit combinations possible if digits can be repeated is 100,000 . Part 3 c. The number of different 5 digit combinations possible if successive digits must be different is 7,290.
Solution
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Math Problem Analysis
Mathematical Concepts
Permutations
Combinations
Counting Principle
Formulas
P(n, r) = n! / (n - r)! for permutations
Total combinations with repetition: 10^5
Total combinations with different successive digits: 10 * 9^4
Theorems
Fundamental Principle of Counting
Suitable Grade Level
Grades 9-12
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