Answer to Question #328610 in Discrete Mathematics for zzd

Question

Number plates in an Arab country consist of 3 letters (chosen from a specified set of 20 letters from the Arabic alphabet) and 4 digits (from 0 to 9).

Find the probability of a plate having identical letters.

Find the probability of a plate having identical digits.

Answer 1

$1:\\20\cdot \frac{1}{20}\cdot \frac{1}{20}\cdot \frac{1}{20}=0.0025\\2:\\10\cdot \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{1}{10}=0.001\\$