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A sequence of length 6 is formed from the digits {0,1,2...9}. If no repetition is allowed, how many of these sequences can be formed if:

f) the sum of the first two terms is 7?

So i set up my place holders:

_ _ _ _ _ _

if the first 2 place holders have a sum of 7, are there 8 possibilities for each place holder because 0+1, 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, 7+0? Or would there be 4 for each consisting only of 0+1, 1+6, 2+5, 3+4? So really teh answer would be 16 x 8P4 or 64 x 8P4?

The answer was 13440, but I don't see why.

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