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
