# 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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