Given the Characters ABCHITUV123 and 4 how many sevencharact

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.) How many if you have to us all four numbers as the first four characters in the password?

Solution

a)

total password can be made= 12C7*7!=3991680

b)

4! *8C3*3! =8064