Question

A license plate is to consist of 3 digits followed by 5 uppercase letters. Determine the number of different license plates possible if the first and second digits must be? odd, and repetition is not permitted. Choose the correcrt answer below. A. 707 comma 266 comma 560 comma 000 B. 7 comma 893 comma 760 C. 1 comma 262 comma 976 comma 000 D. 63 comma 653 comma 990 comma 400 comma 000

Answer 1

We have 5 choices for first place: (1,3,5,7,9)

since repetation is not allowed, for 2nd place our choice will decrease by 1 ,that is becomes 4.

For third place there are 10-2=8 choices, because from (0 to 9, already 2 numbers are assigned to 1st and 2nd place).

For first letter we have 26 choices (A to Z), for 2nd letter we have 25 choices, for 3rd letter we have 24 choices, for 4th letter we have 23 choices, for 5th letter we have 22 choices.

So total number of possible license plates=5*4*8*26*25*24*23*22=1,262,976,000.

oprion C is correct.