Question

customer account “numbers” for a certain company consists of 3 letters followed by 5 single digit numbers. how many different account numbers are possible if repetitions of letters and digits are allowed?

Answer 1

Given:

The number of letters in the account number is, n(A) = 3.

The number of digits in the account number is, n(D) = 5.

The objective is to find the number of possible account numbers with repetitions.

Step-by-step explanation:

The total number of letters is, N(A)=26.

The total number of digits is, N(D)=13.

The formula to find the number of possible numbers are,

`P=N(A)^(n(A))* N(D)^(n(D))\text{ . . . . .(1)}`

To find the number of possibilities:

Substitute the obtained values in equation (1).

`\begin{gathered} P=26^3*10^5 \\ =26*26*26*10*10*10*10*10 \\ =1,757,600,000\text{ ways} \end{gathered}`

Hence, there are 1,757,600,000 ways