SOLUTION: How many distinct permutations can be made from the letters of the word “miscellaneous” that start with “mi”?

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Question 1200107: How many distinct permutations can be made from the letters of the word
“miscellaneous” that start with “mi”?

Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Since the words start with "mi", we only need to find the distinguishable
permutations of "scellaneous" for "mi" can be placed in front of each of them.

If we could tell the two s's apart, the two e's apart, the two l's apart, the
answer would be 11!, but since we cannot tell them apart, we must divide by the
factorial of each of the numbers of the letters that we cannot tell apart.  So the
answer is:

11%21%2F%282%212%212%21%29%22%22=%22%224989600

Edwin

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

To see many other similar  (and different)  solved problems,  look into the lesson
    - Arranging elements of sets containing indistinguishable elements
in this site.

After reading,  your horizon become much wider,  and you will tackle
such problems on your own,  without asking for help from outside.