Can some one please help me with these?

[zac2k4]

I did some problems for homework and these are the only ones i could not get. Thank you in advance.

[h=3]1. How many Different 7 digit phone numbers are pssobile if the first digit cannot be zero or one.(assume no other restrictions and that repetions are allowed)

B. Using the prob above, how many telephone numbers are possible if there are 40 different area codes.

2. How many four digit numbers can be formed to make a number greater than 4000 using 3,4,8,9.
if repetition is not allowed

3. Seven members of the governing board at meetings they are seated in a straight line. How many different seating arrangements are possible if two of the people do not like each other and don't sit next to each other.[/h]

 

[galactus]

I did some problems for homework and these are the only ones i could not get. Thank you in advance.

1. How many Different 7 digit phone numbers are possible if the first digit cannot be zero or one.(assume no other restrictions and that repetitions are allowed)

If the first digit can not be 0 or 1, then there are 8 choices for the first digit. The other 6 have no restrictions, so there are 10 choices for each of those. \(\displaystyle 8\cdot 10^{6}\)

2. How many four digit numbers can be formed to make a number greater than 4000 using 3,4,8,9.
if repetition is not allowed

Think it through. Place the 4 in the first place, then arrange the other 3 digits. Place the 8, then arrange the other 3 digits, and so on. How many ways can you arrange 3 digits?.

3. Seven members of the governing board at meetings they are seated in a straight line. How many different seating arrangements are possible if two of the people do not like each other and don't sit next to each other.

Tie the two people who don't like each other together. Find the number of ways to arrange 7 people in a line. Then, subtract off the number with them tied together.

There are 7! ways to arrange the 7 people in a line. If we tie two particular people together, we have 2 ways to arrange them and 6! ways to arrange the people now (thinking of the two tied together as one person)

\(\displaystyle 2\cdot 6!\) ways to arrange them. \(\displaystyle 7!-2\cdot 6!\)