Question

Customer account "numbers" for a certain company consist of 44 letters followed by 44 numbers.

Step 1 of 2:

How many different account numbers are possible if repetitions of letters and digits are allowed?

Customer account "numbers" for a certain company consist of 44 letters followed by 44 numbers.

Step 2 of 2:

How many different account numbers are possible if repetitions of letters and digits are not allowed?

Answer 1

I think it is not 44 , its 4.

(a) The 44 letters can be chosen in 26 ways each and the 44 numbers in 10 ways each

Number of account numbers possible = 26⁴⁴ * 10⁴⁴

For 4,

The 4 letters can be chosen in 26 ways each and the 4 numbers in 10 ways each

Number of account numbers possible = 26⁴ * 10⁴ = 4569760000

(b) The first letter has 26 options, the second has 25 options, the third has 24 options, the fourth has 23 options. The first number has 10 options, the second number has 9 options, the third number has 8 options.the fourth number has 7 options.

Number of account numbers possible = 26 * 25 * 24 * 23 * 10 * 9 * 8 * 7 = 1808352000.

***please ask if you have any doubts.Happy to help you.Thank you.