The System Administrator has set the following rules for the password:

The password is a string made of 10 characters.

The available characters are Hexadecimal digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

Repetition is allowed unless otherwise stated

1) How many passwords with at least seven As and at least one B, have no adjacent Bs?

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2) How many passwords have exactly two distinct digits? AABBA AAAAB is an example of such string.

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3) How many passwords have six digits from the set 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is allowed) and four digits from the set A, B, C, D, E, F (no repetition is allowed)?

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4) How many passwords have sum of all digits equal to 18? Some examples of such passwords are 0A000 10007, 11226 21111 and 00200 0001F?

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