Can anyone give me a complementary approach to this problem? That is, the calculation of the total minus the "unwanted". Answer: 1050
2026-04-07 05:06:33.1775538393
How many are the anagrams of the word MISSISSIPPI in which there are no two consecutive I letters?
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You can linearly arrange the $7$ non-Is in $${7!\over 4!\cdot2!}=105$$ ways. The generated $7$-letter word has $8$ spaces (inclusive the ends). You can choose $4$ of these spaces for an I in $${8\choose4}=70$$ ways. The total number of admissible $11$-letter words therefore is $105\cdot70=7350$.