Question

1. how many license plates can be made using 3 digits followed by 4 letters if repeated digits and letters are allowed? a) 258336000 b) 456976000 c) 7750008000 d) 1370928000 e) 217002240000 f) none of the above

Explanation:

Step1: Calculate digit possibilities

For each of the 3 digit positions, there are 10 options (0 - 9, since repetition is allowed). So total digit combinations: $10\times10\times10 = 10^3 = 1000$.

Step2: Calculate letter possibilities

For each of the 4 letter positions, there are 26 options (A - Z, repetition allowed). So total letter combinations: $26\times26\times26\times26 = 26^4 = 456976$.

Step3: Total license plates

Multiply digit and letter combinations: $1000\times456976 = 456976000$.

Answer:

B) 456976000