91. In how many ways can the letters in the word МАТЕМАТИКА be rearranged so that the two letters "А" are never next to each other

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91. The word МАТЕМАТИКА, except for the three letters А, contains another 7 letters. They can be rearranged in $7!:(2!\cdot 2!)=1260$ ways. Each such permutation has 8 positions for placing the letter А. Therefore, in each such case, this can be done in $C_{8}^{3}=56$ ways. Finally, we get: $1260 \cdot 56=70560$.