SAT Math Practice Question #26329 - SATify | SATify

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SAT Math Practice Question #26329 - SATify | SATify

#26329

combinatorics

arrangements

Relative Motion

hard

150 sec

How many $12$ -letter arrangements of $4$ A's, $4$ B's, and $4$ C's have no A's in the first $4$ letters, no B's in the next $4$ letters, and no C's in the last $4$ letters?

A.

$\sum_{k = 0}^{4} (k 4)^{3}$

B.

$3^{4} \cdot 2^{4}$

C.

$2^{12}$

D.

$\frac{12 !}{( 4 ! ) ^{3}}$

E.

$3^{12}$