A six-character password consists of three letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? Choose the correct option:
A) 5,040
B) 2,228,720
C) 22,226,000
D) 22,237,440
E) 22,464,000
4 character password: DLDLLD   First digit can be chosen in 10 ways.   The letter can be chosen in 26 ways.   Next digit can be chosen in 9 ways.   The letter can be chosen in 25 ways.   The letter can be chosen in 24 ways.   Next digit can be chosen in 8 ways.   This gives us 10*26*9*25*24*8 ways   Now, the letter can also be DDLLLD so there will be another 10*9*26*25*24*8 ways   Total = 10*26*9*25*24*8*2 = 22,464,000 ways   22,464,000
<result>E</result>
A six-character password consists of three letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?