How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero)?
A) 1,053,000,000
B) 486,000,000
C) 810,000,000
D) 729,000,000
E) 567,000,000

Question

How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero)? ​
A) 1,053,000,000
B) 486,000,000
C) 810,000,000
D) 729,000,000
E) 567,000,000

Quizplus · Accepted Answer

For the four-digit area code, the first digit must be nonzero, which means there are 9 choices (1-9). For the remaining three digits, there are 10 choices (0-9) for each digit, giving us a total of 9x10x10x10 = 9,000 possible area codes.

For the five-digit telephone number, the first digit must be nonzero, which again gives us 9 choices. The remaining four digits can again be any of the 10 digits (0-9). This gives us a total of 9x10x10x10x10 = 90,000 possible telephone numbers.

To get the total number of combinations, we multiply the number of possible area codes by the number of possible telephone numbers: 9,000 x 90,000 = 810,000,000. Therefore, the correct answer is option C.

How Many International Direct-Dialing Numbers Are Possible If Each Number