Question

Determine quantos os anagramas das palavras:

a) MISSISSIPPI;

b) ARARAQUARA;

c) ABOBORA;

d) BISCOITO; ​

Answer 1

Utilizando a permutação com repetição, pois as palavras possui letras repetidas.

(A) $I = 4x \: | \: S = 4x \: | \: P = 2x$

$P = \frac{11!}{4!4!2!}$

$P = \frac{11.10.9.8.7.6.5.4!}{4! \: 4.3.2.2}$

$P = \frac{1.663,200}{48}$

$P = 34,650$

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(B) $A = 5x \: | \: R = 3x$

$P = \frac{10!}{5!3!}$

$P = \frac{10.9.8.7.6.5!}{5! \: 3.2}$

$P = \frac{30,240}{6}$

$P = 5,040$

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(C) $A = 2x \: | \: B = 2x \: | \: O = 2x$

$P = \frac{7!}{2!2!2!}$

$P = \frac{7.6.5.4.3.2!}{2!.4}$

$P = \frac{2520}{4}$

$P = 360$

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(D) $I = 2x \: | \: O = 2x$

$P = \frac{8!}{2!2!}$

$P = \frac{8.7.6.5.4.3.2!}{2!.2}$

$P = \frac{20,160}{2}$

$P = 10,080$