Question

1) Quantos são os anagramas da palavra BARRACA?
(A) 5040.
(B) 2520.
(C) 840.
(D) 420.

Answer 1

$\sf{\underbrace{BARRACA}_{P_7^{3,2}}=\dfrac{7!}{3!\cdot2!}}\\\sf{\dfrac{7\cdot6\cdot5\cdot\diagdown\!\!\!\!</p><p>4^2\cdot\diagdown\!\!\!\!3!}{\diagdown\!\!\!\!</p><p>3!\cdot\diagdown\!\!\!\!</p><p>2}=420}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{alternativa~d}}}}}$