Anagrammi – mateMatica

Il numero di anagrammi di una parola

Tutti i caratteri sono diversi: permutazioni
Ci sono caratteri ripetuti: permutazioni con ripetizioni

Prova ad anagrammare delle parole producendo tutte le permutazioni possibili (anche se ottieni parole senza senso…)

`a`	$\displaystyle P_{1; 1}$	= $\displaystyle \frac{1!}{1!}$	= 1	`a`
`ma`	$\displaystyle P_{2; 1,1}$	= $\displaystyle \frac{2!}{1!\cdot 1!}$	= 2	`am, ma`
`ama`	$\displaystyle P_{3; 2,1}$	= $\displaystyle \frac{3!}{2!\cdot 1!}$	= 3	a₁a₂m, a₂a₁m -> `aam` a₁ma₂, a₂ma₁ -> `ama` ma₁a₂, ma₂a₁ -> `maa`
`amo`	$\displaystyle P_{3; 1,1,1}$	= $\displaystyle \frac{3!}{1!\cdot 1!\cdot 1!}$	= 6	`amo, aom, mao, moa, oam, oma`
`amar`	$\displaystyle P_{4; 2,1,1}$	= $\displaystyle \frac{4!}{2!\cdot 1!\cdot 1!}$	= 12	a₁a₂mr, a₂a₁mr -> `aamr` a₁a₂rm, a₂a₁rm -> `aarm` a₁ma₂r, a₂ma₁r -> `amar` a₁mra₂, a₂mra₁ -> `amra` a₁ra₂m, a₂ra₁m -> `aram` a₁rma₂, a₂rma₁ -> `arma` ma₁a₂r, ma₂a₁r -> `maar` ma₁ra₂, ma₂ra₁ -> `mara` mra₁a₂, mra₂a₁ -> `mraa` ra₁a₂m, ra₂a₁m -> `raam` ra₁ma₂, ra₂ma₁ -> `rama` rma₁a₂, rma₂a₁ -> `rmaa`
`amor`	$\displaystyle P_{4; 1,1,1,1}$	= $\displaystyle \frac{4!}{1!\cdot 1!\cdot 1!\cdot 1!}$	= 24	`amor, amro, aomr, aorm, armo, arom, maor, maro, moar, mora, mrao, mroa, oamr, oarm, omar, omra, oram, orma, ramo, raom, rmao, rmoa, roam, roma`
`mamma`	$\displaystyle P_{5; 3,2}$	= $\displaystyle \frac{5!}{3! \cdot 2!}$	= 10	… -> `aammm` … -> `amamm` … -> `ammam` … -> `ammma` … -> `maamm` … -> `mamam` … -> `mamma` … -> `mmaam` … -> `mmama` … -> `mmmaa`
`amara`	$\displaystyle P_{5; 3,1,1,1}$	= $\displaystyle \frac{5!}{3!\cdot 1! \cdot 1!\cdot 1!}$	= 20	… -> `aaamr` … … -> `rmaaa`
`amare`	$\displaystyle P_{5; 2,1,1,1}$	= $\displaystyle \frac{5!}{2! \cdot 1!\cdot 1!\cdot 1!}$	= 60	… -> `aaemr` … … -> `rmeaa`
`amore`	$\displaystyle P_{5; 1,1,1,1,1}$	= $\displaystyle \frac{5!}{1! \cdot 1!\cdot 1!\cdot 1!\cdot 1!}$	= 120	`aemor, ..., romea`
`errore`	$\displaystyle P_{6;3,2,1}$	= $\displaystyle \frac{6!}{3!\cdot 2!\cdot 1!}$	= 60	… -> `eeorrr` … .. -> `rrroee`
`remore`	$\displaystyle P_{6;2,2,1,1}$	= $\displaystyle \frac{6!}{2! \cdot 2!\cdot 1!\cdot 1!}$	= 180	… -> `eemorr` … … -> `rromee`
`remora`	$\displaystyle P_{6;2,1,1,1,1}$	= $\displaystyle \frac{6!}{2!\cdot 1!\cdot 1!\cdot 1!\cdot 1!}$	= 360	… -> `aemorr` … … -> `rromea`
`remota`	$\displaystyle P_{6; 1,1,1,1,1,1}$	= $\displaystyle \frac{6!}{1!\cdot 1!\cdot 1!\cdot 1!\cdot 1!\cdot 1!}$	= 720	`aemort, ..., tromea`