Aadya is building towers by stacking identically shaped cubes of different colors on top of each other. She has 1 red cube, 2 yellow cubes, 3 green cubes, and 4 blue cubes. How many different 10 -cube-high towers can Aadya build using these 10 cubes so that neither of the bottom two cubes of the tower are green?

So she has 7 options for the base in each tower

 Aug 15, 2022
edited by Jasonkiln  Aug 15, 2022

Step 1: Find the number of ways. Treat this as the "ACCURACY" problem, only we have colors instead of letters. 


Step 2: Find the number of ways there will be 2 green cubes at the bottom. If there are 2 green cubes at the bottom, there are 8 cubes left to order, which consist of 1 red, 2 yellow, 1 green, and 4 blue. Do the same thing as the "ACCURACY" problem. 


Step 3: Subtract the result you got from Step 2 from the result you got from Step 1.

 Aug 15, 2022

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