SOLUTION: a group of math students are given the word QUATTUORDECILLION and challenged to find how many different ways all the letters can be arranged

Putting the 17 letters of QUATTUORDECILLION in alphabetical order,

                          ACDEIILLNOOQRTTUU

If we could distinguish the 2 I's, the 2 L's, the 2 O's, the 2 T's
and the 2 U's, the answer would be 17!.  But since we cannot, we must
reduce 17! by the number of ways each group of indistinguishable 
letters can be arranged within any given permutation. That is, we divide 
by the factorial of the number of times each letter is repeated in the 
word.  Here, 5 letters are repeated each 2 times, so we divide by 2! 
5 times.

Answer:  =  11115232128000

Edwin