Question

O número de anagramas da palavra TABULEIRO é:

A) 120
B) 720
C) 5040
D) 362880
E) 500000​

Answer 1

A aternativa correta é d) 362880

$\large\boxed{\begin{array}{l} \displaystyle \sf Resoluc_{\!\!\!,}\tilde{a} o \\\\\displaystyle \sf para\:sabermos \:a\:quantidade\\\displaystyle \sf de\:anagramas\:que\:a\:palavra\\\displaystyle \sf tabuleiro\:possui\:temos \:que\\\displaystyle \sf\:multiplicar,o\: n\acute{u}mero\:de\\\displaystyle \sf letras \:que\:ela\:possui.\:\\ \sf\end{array}}$

$\large\boxed{\begin{array}{l} \displaystyle \sf C\acute{a}lculo :\\\\\displaystyle \sf tabuleiro \implies9\:letras\\\displaystyle \sf 1\times2\times3\times4\times5\times6\times7\times8\times9=362880\\\\\displaystyle \sf alternativa \:d. \sf\end{array}}$

Answer 2

$\large\boxed{\begin{array}{lr} \sf{tabuleiro\Longrightarrow9 \: letras }\\ \\ \\ 9! = 9×8×7×6×5×4×3×2×1 = \red{362880} \\ \\ \\ \blue{\boxed{\blue{\boxed{\blue{\boxed{ \huge \red{opc_{\!\!,}\tilde{ao}~(D)}}}}}}}\end{array}}$