A password must contain 2 numerals from the list {0,1,2,3,4,5,6,7,8,9} and 2 letters from the list {a,A,b,B,c,C,d,D,e,E}. the first symbol must be a letter. symbols may be repetitive. how many passwords can be generated meeting those conditions? a)1*e5 b)4e5 c)6e5 d)8e5 e)1e6
the correct answer is b how can this computed
I assume that you mean that every password must be exactly four characters long, exactly two of the characters must be a letter from $\{a,A,b,B,c,C,d,D,e,E\}$, the remaining two characters must be a number, the first character must be a letter, and repetition is allowed.
The first character must be a letter, choose which letter
Only one of the remaining three positions will be a letter. Choose which position
Choose which letter occupies that selected position
Choose which number occupies the left-most remaining position
Choose which number occupies the final position
Applying multiplication principle, we get then a final total of $10\cdot 3\cdot 10\cdot 10\cdot 10 = 30000$ possible arrangements.