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Q.

Total number of ways in which the letters of the word ‘MISSISSIPPI’ can be arranged, so that any two S’s are separated?

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a

7350

b

3650

c

6250

d

1261

answer is A.

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Detailed Solution

The word can be written as _M_I_I_I_I_P_P_ and S can have eight positions represented as spaces between the letters. The rest of the seven letters can be arranged in

\frac{7!}{4! 2!}

ways.
Term 7! is divided by 4!2! because "I" is repeated four times and "P" is repeated twice.
The number of ways "S" can be arranged so that none of them connect is

\frac{n!}{r! (n - r)!} = \frac{8!}{4! (8 - 4)!} = \frac{8!}{4! 4!}

Thus, the total number of ways in which the letters of the word "MISSISSIPPI" can be arranged to separate any two S's is

\frac{8!}{4! 4!} \times \frac{7!}{4! 2!} = \frac{8 \times 7 \times 6 \times 5 \times 4!}{4! 4!} \times \frac{7 \times 6 \times 5 \times 4!}{4! 2!} = \frac{352800}{48} = 7350

So, the correct answer is “Option 1”.

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