Math Help - Questions on probability.

1. Questions on probability.

1. You are choosing curtains, paint, and carpet for your room.
You have 12 choices of curtains, 8 choices of paint, and 16 choices
of carpeting. How many different ways can you choose curtains,
paint, and carpeting for your room?

2. Nine books are taken from a shelf and laid in a stack on a
table. In how many different orders can the books be stacked?

3. You have forgotten the combination of the lock on your
school locker. There are 60 numbers on the lock, and the correct
combination is "R___ - L___ - R___." How many possible combinations
are there?

4. If twelve basketball teams are in a tournament, find the
number of different ways that first, second, and third place can be
decided. (Assume there are no ties.)

5. A discussion panel consisting of 4 women and 5 men is to be
seated behind a long table at an open town meeting. In how many
ways can the panel be seated if women and men must be placed in
alternate seats?

6. Next year you are taking math, English, history, world
language, chemistry, physics, and physical education. Each class is
offered during each of the seven periods in the day. In how many
different orders can you schedule your classes?

I think for #1, I multiply all of the numbers? #6, is that 7ncr7? Im not sure about that one. The rest I dont know.

2. Originally Posted by NYCKid09
1. You are choosing curtains, paint, and carpet for your room.
You have 12 choices of curtains, 8 choices of paint, and 16 choices
of carpeting. How many different ways can you choose curtains,
paint, and carpeting for your room?
You have the right idea just multiply the numbers as they are all independent.

Originally Posted by NYCKid09
2. Nine books are taken from a shelf and laid in a stack on a
table. In how many different orders can the books be stacked?
The first book in the stack is 1 of 9, the next is 1 of 8, the third is 1 of 7 etc. So the answer is

$n = 9! = 9 \times 8 \time 7 \times \ldots \times 1$

Originally Posted by NYCKid09
3. You have forgotten the combination of the lock on your
school locker. There are 60 numbers on the lock, and the correct
combination is "R___ - L___ - R___." How many possible combinations
are there?
Assuming the same number is successive parts of the code are valid. then you have 3 independent choices of 60 so

$n = 60^3$

Originally Posted by NYCKid09
4. If twelve basketball teams are in a tournament, find the
number of different ways that first, second, and third place can be
decided. (Assume there are no ties.)
This is like the book stack problem but you need just an arrangement of 3 from twelve. First is 1 of 12 second is 1 of 11 and third is 1 of 10. So

$n = 12 \times 11 \times 10 = \frac{12!}{(12-3)!}$.

Originally Posted by NYCKid09
5. A discussion panel consisting of 4 women and 5 men is to be
seated behind a long table at an open town meeting. In how many
ways can the panel be seated if women and men must be placed in
alternate seats?
You can consider the men and women to be independent since there is an odd number and they must alternate the men have to sit on the ends.

So you have 5! arrangements of the men and 4! arrangements of the women which are independent and so the total answer is

$n = 5! \times 4!$

Originally Posted by NYCKid09
6. Next year you are taking math, English, history, world
language, chemistry, physics, and physical education. Each class is
offered during each of the seven periods in the day. In how many
different orders can you schedule your classes?
You have to take each one over the course of the day. There are seven periods and seven subjects so this is just like the book stack problem.

$n = 7!$

Hope this helps.