How many arrangements can be made by the letters of the word DEFINITION a) if the letters i do not occupy the first or last place, (ii) if the letters i are together?

Question

paxpolaris · Answer

total 10 letters with 3-i,2-N

anonymous · Answer

oh actually i figured out how to do a)
i just need help with b) now

paxpolaris · Answer

b) the number of anagrams possible of DEFNNOT *8

paxpolaris · Answer

or just think of the 3 i's as 1 i

anonymous · Answer

oh ok thanks

paxpolaris · Answer

I got:
a) 141,120
b)   20,160

anonymous · Answer

could you please show me your working for b) please
thank you in advance!

paxpolaris · Answer

If you think of the 3-i's together as a single letter ... you have 8 letters with N repeating 2 times: $$= {8! \over 2!}$$