5 kids can divide themselves up into groups of two 10 ways. They can also divide themselves up into groups of three 10 ways. How do you explain the connection between the two answers?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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5 kids can divide themselves up into groups of two 10 ways. They can also divide themselves up into groups of three 10 ways. How do you explain the connection between the two answers?

(I'm asking this again bcuz the first two times I asked it, yall didn't answer the question.) Im asking WHY is 5 kids divided into groups of two 10 but groups of three is also ten. not how to solve it. why are both answers ten? is there a reason?

Expert Solution
Step 1

Combination Rule:

The arrangement of r objects from n different objects is given by:

Probability homework question answer, step 1, image 1

One of the properties of combination is nCr = nCn-r

Step 2

That is, 

Probability homework question answer, step 2, image 1

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