How many different 6-digit license plates are possible if the first 3 digits can be any letter and the last 3 digits can be any number? A. 108
B. 17,576,000
C. 128
D. 15,725,000

B

Step-by-step explanation:

every position on the license plate is independent from the others.

so, for each position we have the full choice of all possibilities.

there are 26 letters in the alphabet. and there are 10 different single numeric digits.

so, for the first position we have 26 possibilities. as we have for the second and third positions.

the means for each option for the first position we have 26 choices for the second.

that is 26×26.

then for each given choice of the first 2 positions we have 26 choices for the third position.

that is then 26×26×26 possibilities.

for each of the given choices of the first 3 positions we have 10 choices on the fourth position. and then on the fifth and the sixth positions.

the makes altogether

26×26×26×10×10×10

even without calculator I know it must be B, because the number of possibilities must end with 3 "0"s (due to the 10×10×10).

and the main number block must end with a "6" due to 26×26×26, which means for the last position we only need to consider 6×6×6. 6×6 = 36 ending in a "6". and that again multiplied by 6 is again 36 ending in a "6".

so, 26×26×26 has to end with a "6". that gives us B.

47 - 90 = 43

43 - 180 = x

x = 137