Michelle knows that there are 8!/2!2! permutations of her name when ALL the letters are used.
She would like to know how many permutations there are if ANY NUMBER OF LETTERS in her name are used.
this is what i have figured out so far.
if she uses all letters in her name then there are 8! ways.
if she uses 7 then there are 8!/1! ways
if she only uses 6 letters there are 8!/2! ways
if she uses only 5 letters there are 8!/3! ways
if she uses only 4 letter there are 8!/4! ways
if she uses 3 letter there are 8!/5! ways
if she uses 2 letters there are 8!/6!
and if she uses only one letter there are 8 options .
and then all products are added because they are mutually exclusive.
to me ANY NUMBER OF LETTERS mean that she can use any number of letters in her name. she doesn't have to use all 8.