SAT Math Practice Question #26328 - SATify | SATify

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SAT Math Practice Question #26328 - SATify | SATify

#26328

combinatorics

arrangements

Relative Motion

hard

150 sec

How many $9$ -letter arrangements of $3$ A's, $3$ B's, and $3$ C's have no A's in the first $3$ letters, no B's in the next $3$ letters, and no C's in the last $3$ letters?

A.

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

B.

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

C.

$2^{9}$

D.

$\frac{9 !}{( 3 ! ) ^{3}}$

E.

$3^{9}$