Question

At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825.

Answer 1

Answer:

Part A) The total different phone numbers are 20,000

Part B) The total numbers in which the last four digits are all different is 10,080

Step-by-step explanation:

Consider the provided information.

At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825.

Part (a) How many different phone numbers are possible?

If the numbers are start with 824:

The total digits are 7 out of which 3 are fixed (i.e 824).

For rest of 4 digits we have 10 digits.

10×10×10×10=10,000

If the numbers are start with 825:

The total digits are 7 out of which 3 are fixed (i.e 825).

For rest of 4 digits we have 10 digits.

10×10×10×10=10,000

Hence, the total number of ways are: 10,000+10,000=20,000

(b) How many different phone numbers are there in which the last four digits are all different?

If the numbers are start with 824:

The total digits are 7 out of which 3 are fixed (i.e 824).

Rest 4 digits should be different. That means if we select any number the next number must be other than the selected number and same for the rest of the numbers.

10×9×8×7=5,040

If the numbers are start with 825:

The total digits are 7 out of which 3 are fixed (i.e 825).

Rest 4 digits should be different.

10×9×8×7=5,040

Hence, the total number of ways are: 5,040+5,040=10,080