Answer to Question #142095 in Discrete Mathematics for Promise Omiponle

Question

(2) How many different license plates can be made consisting of 10 characters if the first 5 characters consist of uppercase English letters, while the final 5 characters are digits?

Answer 1

Considering that the repetition of alphabets and numbers is allowed in the license plates we can find the number of possibilities as under:-

Since there are total 5 positions for alphabets & 5 positions of numbers the total number of possibilities = ²⁶C₁*²⁶C₁*²⁶C₁*²⁶C₁*²⁶C₁*¹⁰C₁*¹⁰C₁*¹⁰C₁*¹⁰C₁*¹⁰C₁*

=26*26*26*26*26*10*10*10*10

=26⁵*10⁵

Total 26⁵*10⁵ different license plates can be made consisting of 10 characters if the first 5 characters consist of uppercase English letters, while the final 5 characters are digits.