SOLUTION: how many distinct permutations can be made from the letters of the word "mathematics".

Algebra ->  Probability-and-statistics -> SOLUTION: how many distinct permutations can be made from the letters of the word "mathematics".       Log On


   

Question 849368: how many distinct permutations can be made from the letters of the word "mathematics".
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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