License plates consist of letters and/ or digits. Calculate the number of licence plates that could be formed in each province or territory. Assume all numbers and letters are possible.
a) Ontario, with 4 letters followed by 3 digits
b)Québec, with 3 letters followed by 3 digits
c)Northwest Territories, with 6 digits
assume 26 letters options and 10 digit options
therefore:
a) (26^4)(10^3)= 456 976 000
b) (26^3)(10^3)= 17 576 000
c) 10^6= 1 000 000
a) Ontario, with 4 letters followed by 3 digits:
To calculate the number of license plates in Ontario, we need to consider that there are 26 letters in the English alphabet and 10 digits. So, for the 4 letters, we have 26 options each time, and for the 3 digits, we have 10 options each time. Therefore, the total number of license plates in Ontario would be 26^4 * 10^3. That's a lot of possibilities! It's like trying to find a needle in a haystack, except in this case, the haystack is made entirely of needles.
b) Québec, with 3 letters followed by 3 digits:
Similar to Ontario, we have 26 options for each of the 3 letters and 10 options for each of the 3 digits. Therefore, the total number of license plates in Québec would be 26^3 * 10^3. If this were a race, it would be like having 26 speedy cheetahs running alongside 10 racing cars. It's a wild combination!
c) Northwest Territories, with 6 digits:
In this case, we only have digits, so we have 10 options for each of the 6 digits. Therefore, the total number of license plates in the Northwest Territories would be 10^6. Just imagine the amount of numbers you can come up with! It's like trying to find the biggest number in the universe. Good luck with that!
Remember, these calculations assume all numbers and letters are possible. I hope you enjoy your virtual license plate hunt!
a) For Ontario license plates with 4 letters followed by 3 digits, we have:
- For each letter, there are 26 possibilities (from A to Z).
- For each digit, there are 10 possibilities (from 0 to 9).
Therefore, the number of license plates that could be formed in Ontario is:
26 * 26 * 26 * 26 * 10 * 10 * 10 = 45,697,600
b) For Québec license plates with 3 letters followed by 3 digits, we have:
- For each letter, there are 26 possibilities (from A to Z).
- For each digit, there are 10 possibilities (from 0 to 9).
Therefore, the number of license plates that could be formed in Québec is:
26 * 26 * 26 * 10 * 10 * 10 = 17,576,000
c) For Northwest Territories license plates with 6 digits, we have:
- For each digit, there are 10 possibilities (from 0 to 9).
Therefore, the number of license plates that could be formed in Northwest Territories is:
10 * 10 * 10 * 10 * 10 * 10 = 1,000,000
To calculate the number of possible license plates for each province or territory, we need to determine the total number of possible combinations of letters and/or digits.
a) Ontario:
In Ontario, the license plates consist of 4 letters followed by 3 digits. Since both letters and digits are possible, we have 26 choices for each letter and 10 choices for each digit.
The total number of possible license plates in Ontario would be calculated as:
Number of possible letters * Number of possible letters * Number of possible letters * Number of possible letters * Number of possible digits * Number of possible digits * Number of possible digits
In this case, it would be: 26 * 26 * 26 * 26 * 10 * 10 * 10 = 456,976,000 possible license plates.
b) Québec:
In Québec, the license plates consist of 3 letters followed by 3 digits. Similarly, we have 26 choices for each letter and 10 choices for each digit.
The total number of possible license plates in Québec would be calculated as:
Number of possible letters * Number of possible letters * Number of possible letters * Number of possible digits * Number of possible digits * Number of possible digits
In this case, it would be: 26 * 26 * 26 * 10 * 10 * 10 = 17,576,000 possible license plates.
c) Northwest Territories:
In Northwest Territories, the license plates consist of 6 digits. Since only digits are allowed, we have 10 choices for each digit.
The total number of possible license plates in Northwest Territories would be calculated as:
Number of possible digits * Number of possible digits * Number of possible digits * Number of possible digits * Number of possible digits * Number of possible digits
In this case, it would be: 10 * 10 * 10 * 10 * 10 * 10 = 1,000,000 possible license plates.