Answer
3991680 and
$8064$
Work Step by Step
Given the characters A, B, C, H, I, T, U, V,
1, 2, 3, and 4, how many seven-character passwords can be made? (No repeats are allowed.)
Use permutation, $_{12}P_7$=3991680
How many if you have to use all four numbers as the first four characters in the password?
For the first four places, we have $4!=24$ choices.
For the last 3 places, we have $_8P_3$=336 variations.
The total is the product of the two: $24\times336=8064$
