Question 849368
the word mathematics has:


11 letters in total
2 of the letter 'a'
2 of the letter 'm'
2 of the letter 't'


i believe that's all the duplicates.


the permutation formula is 11! / (2! * 2! * 2!)


this becomes 11! / 8 which is equal to 4,989,600.


you take the permutation of the whole number and you divide by the permutation of each of the duplicates.


for example:


consider the letters ABC.


the permutation of these is 3! = 6.


those permutations are:


ABC
ACB
BAC
BCA
CAB
CBA


now consider the permutation of the letters AAC.


use the formula given above and you get 3! / 2! which is equal to 6/2 = 3.


those permutations are:


AAC
ACA
CAA