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