Math Problem Statement

from the figure 1 2 3 4 5 6 7, how many 4 digit numbers can be formed with no figure being used moer than once in each number? of these 4-digit numbers formed, how many are divisible by 3

Solution

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Divisibility Rules
Modular Arithmetic

Formulas

n! (for counting permutations)
Divisibility by 3 rule: A number is divisible by 3 if the sum of its digits is divisible by 3

Theorems

Pigeonhole Principle
Divisibility Rule for 3

Suitable Grade Level

Grades 7-9