Answer
$453,600$ distinguishable permutations.
Work Step by Step
2 B's, 2 A's, 2 L's, 1 S, 1K, 1 E, 1T. Total: 10 letters.
$\frac{10!}{2!\times2!\times2!\times1\times1\times1\times1}=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{8}=453,600$
