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The first can be any one of 10 digits. For each of those . . .

The second can be any one of the nine digits not the same as the first. For each of those . . .

The third can be any one of the nine digits not the same as the second. For each of those . . .

The fourth can be any one of the nine digits not the same as the third. For each of those . . .

The fifth can be any one of the nine digits not the same as the fourth. For each of those . . .

The sixth can be any one of the nine digits not the same as the fifth. For each of those . . .

The seventh can be any one of the nine digits not the same as the sixth. For each of those . . .

The eighth can be any one of the nine digits not the same as the seventh. For each of those . . .

The ninth can be any one of the nine digits not the same as the eighth.

The total number of possibilities is: (10 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9) = 430,467,210 .

If matching adjacent digits were allowed there would be 1,000,000,000 possibilities.

So the restriction has eliminated 56.95% of them.

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Q: How many combinations of 9 digits are possible if no two adjacent digits are the same?
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