Logic, Sets, and Counting Techniques (telephone area codes)?

Telephone area codes in the U.S. consists of 3 digits (MD 301, VA 703, DC 202) First digit in the area code was from 2 to 9, the second was either 0 or 1, and the third could be any digit except 0.

a) according to these rules, how many different area codes began with the digit 3?

b) how many different area codes ended with the digit 2?

c)how many differnet area codes are possible?



If the rules changed to, the first digit in the area code is from 2 to 9, the second digit is from 0 to 8, the third digit is from 0 to 9

d)according to the new rule, how many different area codes can begin with the digit 3?

e)how many different area codes are now possible?Logic, Sets, and Counting Techniques (telephone area codes)?
The General Counting Principle states that if different trials can be done in a certain number of ways each time, then the number of possible outcomes is found by multiplying the number of possibilities for each trial.



a) There are

1 way for the first digit (3)

2 ways for the second (0 or 1)

9 ways for the third (1-9)



So in total 1*2*9 = 18 ways.



b) There are

8 ways for the first digit (2-9)

2 ways for the second (0 or 1)

1 way fo the third (2)



In total 8*2*1 = 16 ways.



c) There are

8 ways for the first

2 for the second

9 for the third.



8*2*9 = 144 ways.



d) There are

1 way for the first (3)

9 ways for the second (0-8)

10 for the third (0-9)



1*9*10 = 90 ways.



e) There are

8 ways for the first (2-9)

9 for the second (0-8)

10 for the third (0-9)



8*9*10 = 720 ways.