How many different license plates begin with 2 letters followed by 4 digits then followed by 1 more letter? Assume no letters or digits are repeated.

Question

Answer Choices

A)175,760,000

B)26! x 10!

C)720,000

D)78,624,000

Please use step by step explanation

Answer 1

There are 26 letters and 10 digits available to begin with. If there are no repetitions then:

There are 26 letter available for the first letter

25 letters available for the 2nd letter

There are 10, 9, 8 and 7 numbers available for the next 4 digits

There are 24 letters available for the last letter.

Based on the counting principle there are 26 * 25 * 10 * 9 * 8 * 7 * 24 = 78,624,000 (D) combinations.