Question

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?

Answer 1

Using the Fundamental Counting Theorem, it is found that Aadya can build 1,693,440 cube towers.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

Considering that she has 10 cubes, and the bottom and top cubes cannot be green, the parameters are given by:

$n_1 = 7, n_10 = 6, n_2 = 8, n_3 = 7, \cdots n_9 = 1$

Hence the number of cubes is given by:

N = 7 x 6 x 8! = 1,693,440.

Aadya can build 1,693,440 cube towers.

More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866

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