Question

Usando permutação com repetição, permute a palavra ORNITORRINCO.​

Answer 1

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$\sf\underbrace{\sf ORNITORRINCO}_{\sf P_{12}^{3,3,2,2}}=\dfrac{12!}{3!\cdot3!\cdot2!\cdot2!}\\\sf P_{12}^{3,3,2,2}=\dfrac{12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot\diagdown\!\!\!\!\!6\cdot5\cdot\diagdown\!\!\!\!4\cdot\diagdown\!\!\!\!\!\!3!}{\diagdown\!\!\!\!3!\cdot\diagdown\!\!\!\!\!6\cdot\diagdown\!\!\!2\cdot\diagdown\!\!\!2}\\\sf P_{12}^{3,3,2,2}=12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot5\\\huge\boxed{\boxed{\boxed{\boxed{\sf P_{12}^{3,3,2,2}=3326400}}}}\blue{\checkmark}$