Math Problem Statement

In how many ways can 30 balls of 10 different colors, 3 identical ball of each color, be randomly distributed in 10 similar boxes?

Solution

To determine the number of ways to distribute 30 balls of 10 different colors (with each color having 3 identical balls) into 10 identical boxes, we need to consider both the constraints of identical balls of the same color and the identical boxes.

Step-by-Step Solution:

  1. Total Number of Balls: We have a total of 30 balls (since 10×3=3010 \times 3 = 30).

  2. **

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Distribution problems
Factorials

Formulas

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Theorems

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Suitable Grade Level

Grades 10-12

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