Question

Customer account "numbers" for a certain company consist of 3 letters followed by 2 numbers.Step 1 of 2 : How many different account numbers are possible if repetitions of letters and digits are allowed?

Answer 1

Answer with explanation:

Number of Distinct Letters in English Alphabet = 26 Capital +26 Small

                                                 =52 Alphabets

Total Number of Distinct digits in number system = {0,1,2,3,4,5,6,7,8,9}=10

Account Number of Customers for a certain Company =3 Letters +2 Numbers

Out of 52 Alphabets , 3 Letters can be Chosen in

    $=_{3}^{52}\textrm{P}$ ways, since Order of arranging of three alphabets is Important.

Similarly, out of 10 Digits , 2 numbers can be chosen in

      $=_{2}^{10}\textrm{P}$ ways, since Order of arranging of three alphabets is Important.

Total Number of Possible Account number

         $=_{3}^{52}\textrm{P} \times _{2}^{10}\textrm{P}\\\\=\frac{52!}{(52-3)!}\times \frac{10!}{(10-2)!}\\\\=\frac{52!}{(49)!}\times \frac{10!}{(8)!}\\\\=52\times 51 \times 50 \times 9 \times 10\\\\=11934000$