Given word is MISSISSIPPI,
Here, I occurs 4 times, S = 4 times
P = 2 times, M = 1 time
So, we write it like this _M_I_I_I_I_P_P_
Now, we see that spaces are the places for letter S, because no two S can be together
So, we can place 4 S in these 8 space in \(^8C_4\) ways.
and we can arrange other 7 letters in \(7!\over 4!2!\) ways.
Hence, total number of words can be formed = \(^8C_4\) \(\times\) \(7!\over 4!2!\)
= 7. \(^8C_4\) . \(^6C_4\)
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is