Solve the problem.
-A license plate is to consist of 6 digits followed by 2 letters. Determine the number of different license plates possible if the first and fifth digits must be odd, and repetition is not permitted.
A)27,300,000
B)2350
C)109,200,000
D)21,840,000

Question

Quizplus · Accepted Answer

For the first slot, there are 5 odd digits to choose from. For the fifth slot, there are 4 odd digits left to choose from (since repetition is not allowed). For the second, third, fourth, and sixth slots, there are 5, 4, 3, and 2 choices respectively (since repetition is not allowed). For the letters, there are 26 choices for each slot.

Therefore, the total number of possible license plates is:

5 * 5 * 4 * 5 * 3 * 2 * 26 * 26 = 21,840,000 There are 5 choices for the first digit (1, 3, 5, 7, 9) and 5 choices for the fifth digit (since it cannot be the same as the first). For the second, third, fourth, sixth, and seventh digits, there are 5, 8, 7, 6, and 26 choices, respectively. (For the second digit, there are 5 choices since it cannot be the same as the first digit; for the third digit, there are 8 choices since it cannot be the same as the first two digits; for the fourth digit, there are 7 choices since it cannot be the same as the first three digits; for the sixth digit, there are 6 choices since it cannot be the same as any of the previous 5 digits; for the seventh digit, there are 26 choices since it can be any letter of the alphabet.) Therefore, the total number of license plates is 5 × 5 × 8 × 7 × 6 × 26 = 21,840,000.

Solve the Problem. -A License Plate Is to Consist of 6 Digits Followed