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Home » Therefore, there are \(\boxed60\) ways to choose and arrange 3 minerals from 5. - Imagemakers

Therefore, there are \(\boxed60\) ways to choose and arrange 3 minerals from 5. - Imagemakers

📅 May 2, 2026 👤 scraface

May 02, 2026

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To place 3 non-adjacent A’s in 8 positions, we use the combinatorial m...
This is equivalent to placing 3 A’s and 5 non-A’s, with at least one n...
To count the number of ways to place 3 non-adjacent A’s in 8 positions...
We use the stars and bars transformation: if we place 3 A’s with at le...
This is now equivalent to distributing 3 indistinct items (remaining n...
But since the non-A positions (the 5 positions not occupied by A) are...
Alternative ( clearer) approach:
The number of ways to choose 3 non-adjacent positions out of 8 is a kn...
This is given by:
\binom{8 - 3 + 1}{3} = \binom{6}{3} = 20

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