How many different words can be formed by jumbling the letters in the word ‘MISSISSIPPI’ in which no two S are adjacent ?

Solution :

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. \(^8C_4\) . \(^6C_4\)

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