Question

How many different license plates can be made if it is one letter, followed by two digits, followed by two letters if no letter or number can be repeated?

A) 1,000,000
B) 1,625,000
C) 500,000
D) 2,000,000

Answer 1

1,625,000 different license plates can be made if it is one letter, followed by two digits, followed by two letters if no letter or number can be repeated.The correct option is B) 1,625,000.

Step-by-step explanation:

The number of different license plates can be calculated by considering the constraints on each position. For the first letter, there are 26 choices (A-Z), for the two digits, there are 10 choices for each digit (0-9), and for the last two letters, there are again 26 choices for each. Applying the multiplication rule for counting, the total number of possible combinations is given by:

`\[26 * 10 * 10 * 26 * 26 = 1,625,000.\]`

This accounts for the restriction that no letter or number can be repeated in the license plate. The first position can be filled in 26 ways, the second in 10 ways, the third in 10 ways, the fourth in 26 ways, and the fifth in 26 ways. Multiplying these possibilities gives the total count.

Therefore, the correct answer is option B) 1,625,000, reflecting the total number of unique license plates that can be formed under the given constraints. It is crucial to consider these constraints systematically to arrive at the accurate count of possibilities.

The correct option is B) 1,625,000.