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11 Feb 2025, 22:07
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State A: \(26^2∗9^4∗23\)
State B: \(\frac{26^3∗9^4}{26}\)
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (02:35) correct
28%
(02:52)
wrong
based on 546
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Two states have different rules for letter and number combinations for vehicle license plates. In State A, a license plate has 7 digits. The first 3 digits are letters but the first letter cannot be an A, B or C. The remaining digits are all numbers and zeros are not allowed. In State B, a license plate has 6 digits. The first 2 digits are letters and can be any letter. The remaining digits are all numbers and zeros are not allowed.
In the table, under column A, select the expression that represents the number of possible combinations of license plates in State A and under column B, select the expression that represents the number of possible combinations of license plates in State B. Make two selections, one in each column.
In the table, under column A, select the expression that represents the number of possible combinations of license plates in State A and under column B, select the expression that represents the number of possible combinations of license plates in State B. Make two selections, one in each column.
| State A | State B | |
| \(26^2∗9^3\) | ||
| \(\frac{26^3∗9^4}{26}\) | ||
| \(26^3∗9^4-3\) | ||
| \(26^3∗9^4∗3\) | ||
| \(26^3∗9^4∗23\) | ||
| \(26^2∗9^4∗23\) |
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Official Answer
State A: \(26^2∗9^4∗23\)
State B: \(\frac{26^3∗9^4}{26}\)
11 Feb 2025, 22:34
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State A
Answer: \(23* (26)^2 * 9^4\)
State B
Answer: \((26)^2 * 9^4\)
| Letter 1 | Letter 2 | Letter 3 | Digit 1 | Digit 2 | Digit 3 | Digit 4 |
| 23 | 26 | 26 | 9 | 9 | 9 | 9 |
| All letters - 3 | All letters | All letters | 1-9 | 1-9 | 1-9 | 1-9 |
Answer: \(23* (26)^2 * 9^4\)
State B
| Letter 1 | Letter 2 | Digit 1 | Digit 2 | Digit 3 | Digit 4 |
| 26 | 26 | 9 | 9 | 9 | 9 |
| All letters | All letters | All digits -0 | 1-9 | 1-9 | 1-9 |
Answer: \((26)^2 * 9^4\)
18 Feb 2025, 12:35
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1. Each state has different rules for the license plates, giving us a different number of combinations to calculate. Let's solve the question for each state.
2. It is important to note that the alphabet has 26 letters overall.
3. State A.
- The first digit has to be a letter, but not A, B, or C. This leaves 26 - 3 = 23 combinations.
- The next two digits must also be letters, with no restrictions. This is 26 \(*\) 26.
- The other 4 digits are numbers 1 through 9, giving us 9 \(*\) 9 \(*\) 9 \(*\) 9.
The total number of combinations will be \((23) * (26 * 26) * (9 * 9 * 9 * 9) = 23 * 26^2 * 9^4\), which is closest to the answer choice \(26^2 * 9^4 * 23\).
4. State B.
- The first two digits must be letters, with no restrictions. This gives 26 \(*\) 26.
- The other 4 digits are numbers 1 through 9, giving us 9 \(*\) 9 \(*\) 9 \(*\) 9.
The total number of combinations will be \((26 * 26) * (9 * 9 * 9 * 9) = 26^2 * 9^4\), which is closest to the answer choice \(\frac{26^3}{26} * 9^4\).
5. Our answer will be: State A - \(26^2 * 9^4 * 23\) and State B - \(\frac{26^3}{26} * 9^4\).
2. It is important to note that the alphabet has 26 letters overall.
3. State A.
- The first digit has to be a letter, but not A, B, or C. This leaves 26 - 3 = 23 combinations.
- The next two digits must also be letters, with no restrictions. This is 26 \(*\) 26.
- The other 4 digits are numbers 1 through 9, giving us 9 \(*\) 9 \(*\) 9 \(*\) 9.
The total number of combinations will be \((23) * (26 * 26) * (9 * 9 * 9 * 9) = 23 * 26^2 * 9^4\), which is closest to the answer choice \(26^2 * 9^4 * 23\).
4. State B.
- The first two digits must be letters, with no restrictions. This gives 26 \(*\) 26.
- The other 4 digits are numbers 1 through 9, giving us 9 \(*\) 9 \(*\) 9 \(*\) 9.
The total number of combinations will be \((26 * 26) * (9 * 9 * 9 * 9) = 26^2 * 9^4\), which is closest to the answer choice \(\frac{26^3}{26} * 9^4\).
5. Our answer will be: State A - \(26^2 * 9^4 * 23\) and State B - \(\frac{26^3}{26} * 9^4\).
