required information\nlicense plates in a certain state consist of three letters followed by three…
required information\nlicense plates in a certain state consist of three letters followed by three digits.\nhow many license plates are there that contain neither the letter \q\ nor the digit \9\?
Answer
Explanation:
Step1: Count valid letter options
Total letters: 26. Exclude "Q", so valid letters: $26 - 1 = 25$
Step2: Calculate 3-letter combinations
Each position has 25 choices. So: $25 \times 25 \times 25 = 25^3 = 15625$
Step3: Count valid digit options
Total digits: 10. Exclude "9", so valid digits: $10 - 1 = 9$
Step4: Calculate 3-digit combinations
Each position has 9 choices. So: $9 \times 9 \times 9 = 9^3 = 729$
Step5: Total valid license plates
Multiply letter and digit combinations: $15625 \times 729$
Answer:
11390625