1. 6-Number PIN Code: - For a 6-number PIN code, each digit can be any number from 0 to 9. - Therefore, the total number of possible PIN codes is 106=1,000,000.
2. 11-Digit Cellphone Numbers: - Given each number begins with 0998, it is a fixed prefix. - For the remaining 7 digits, each can be any number from 0 to 9. - Thus, the total number of possible 11-digit cellphone numbers is 107=10,000,000.
3. Car License Plates: - For license plates with 2 different letters followed by 3 different digits: - Total number of ways to choose 2 letters from the 26 letters in the alphabet: 26×25 - Total number of ways to choose 3 digits from 0 to 9: 10×9×8 - The total number of possible car license plates is 26×25×10×9×8.
4. 4-Digit Even Numbers: - Given digits 5, 6, 7, 8, 9 with no repetition: - Hundreds place can be filled with 6 or 8. - Units place can be filled with any of the remaining digits. - Tens and thousands place can be filled in any order with the remaining digits.
- Total number of possible 4-digit even numbers is 2×4×3×2=48. 5. True or False Test: - For each question, there are 2 choices (True or False). - Therefore, the total number of ways to mark answers on a 10-question true or false test is 210=1024. These calculations provide the total number of possibilities for each of the given scenarios
Answer:
1: There are 1,000,000 possible 6-digit PIN codes.
2: There are 10,000,000 possible 11-digit cellphone numbers that can be formed if each cell number begins with 0998
3: 676,000 possibilities
4: 360 (I think)
5:1 024