How many different words can be formed by jumping the letter in the word $M I S S I S S I P P I$ in which no two $S$ are adjacent?

{7.}^{6} C_{4} .^{7} C_{4}

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{6.7}^{7} C_{4}

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{6.8}^{7} C_{4}

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{7.}^{6} C_{4} .^{8} C_{4}

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Solution

The correct option is A ${7.}^{6} C_{4} .^{7} C_{4}$
We have word $= M I S S I S S I P P I$
in this word there are $4 I^{'} s, 4 S^{'} s, 2 P^{'} s$ and $1 M$
No two $S$ should be together.
$∴$ $S$ at this places $- M - I - I - I - I - P - P -$
$∴$ possible No. of words $= \frac{^{8} C_{4} .7!}{4.2!} = 7^{8} C_{4}^{6} C_{4}$ .
$= 7 \times 70 \times 15 = 7350$ Ans

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