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

If 3 letters are followed by 2 numbers and repetitions are allowed, there are a total of 1757600 possible different account numbers. Each letter position has 26 choices and each number position has 10 choices.

Step-by-step explanation:

The student has asked to determine the number of different customer account "numbers" a company can have if the accounts consist of 3 letters followed by 2 numbers, with repetitions allowed for both letters and numbers.

To calculate the total number of possible account numbers, we can use the multiplication principle of counting. The number of options for each position of the account number is multiplied together to get the total number of combinations.

For the 3 letters, each position can contain any letter from A-Z, which gives us 26 choices per position. Since repeats are allowed, each of the 3 positions has 26 possible choices.

For the 2 numbers, each position can contain any digit from 0-9, which gives us 10 choices per position.

Therefore, to find the total number of possible account numbers, we calculate:

26 × 26 × 26 × 10 × 10 = 1757600 possible account numbers.

Answer 2

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} * _(2)^(10)\textrm{P}\\\\=(52!)/((52-3)!)* (10!)/((10-2)!)\\\\=(52!)/((49)!)* (10!)/((8)!)\\\\=52* 51 * 50 * 9 * 10\\\\=11934000`