the number of arrangements that can be formed by taking all the letters of the word $MISSISIPPI$ so that all $S$'s comes together is

The word MISSISIPPI contains 11 letters total: 4 S's, 4 I's, 2 P's, and 1 M. Grouping the four S's together as a single entity reduces the total items to arrange to 8, consisting of the S-block, 4 I's, 2 P's, and 1 M. The number of permutations of these 8 items is calculated using the formula for indistinguishable items, giving 8!/(4!2!). This simplifies exactly to (8 x 7 x 6 x 5 x 4!) / (4! x 2 x 1), which results in 6!2!.

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