Answer:
Step-by-step explanation:
Permutation has to do with arrangement.
To form different word by rearranging the word KINDNESS, this can be done in the following way;
The total letters present in kindness = 8 letters
Repeated letters are 2N's and 2S's
The arrangement is done in [tex]\frac{8!}{2!2!}[/tex] ways
[tex]= \frac{8!}{2!2!} \\= \frac{8*7*6*5*4*3*2!}{2!*2}\\ = 8*7*3*5*4*3\\= 10,080 \ different\ words[/tex]
For MATHEMATICIAN;
The total letters present in kindness = 13 letters
Repeated letters are 2M's, 2T'S 2I'sand 3A's
The number of words formed =
[tex]\frac{13!}{2!2!2!3!} \\= \frac{13*12*11*10*9*8*7*6*5*4*3!}{6*3!}\\= 13*2*11*10*9*8*7*6*5*4\\= 172,972,800\ different\ words[/tex]
