Why is it wrong - Combinatorics

Q1: How many ways to select 5 kids from 25 kids?
Solution:
Correct answer: 25C5 = 25!/5!20!

But what if I do it like this:
First select 1 kid from 25: 25C1
Then select 4 from remaining 24: 24C4
Final answer: 25C1*24C4 = 25!/4!20!

What is wrong here?
The problem is this:
When you do 25C1, let's say you selected 'A'.
Then when you select 4 kids from 24, you could choose 'B','C','D','E'.
But you could also choose 'B' first and then 'A','C','D','E'.
And both would give you same result.
So you are overcounting by a factor of 5.

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