1. Looks like the same formula you have right below it for combinations. Run a search for "combination" on the board, and you'll find a lot of examples.

And no, n!/k!(n-k)! is not the same as n/(n-k). Just plug in some values, and you'll see.

The "!" represents a factorial. 6! = 1 x 2 x 3 x 4 x 5 x 6. 4! = 1 x 2 x 3 x 4. You get the idea.

For combinations, n = the number of available options. k = the desired number you have to choose.

Let's look at a very simple example, look at selecting jurors for a jury. There are 3 jurors, and you have to pick 2. How many different combinations are available?

First, let's look at the tried, true, and tiresome job of writing it out.
If we label our jurors as A, B, and C, here are the combinations:
A, B
A, C
B, C

That's three possible combinations. Now, this method of writing it out becomes very tedious and time consuming. So, you should use the combination formula.

nCk = n! / (k! (n-k)!)
3C2 (said as "three choose two") = 3! / ((2!)((3-2)!))
3! = 3x2x1 = 6
2! = 2x1 = 2
(3-2)! = 1! = 1x1 = 1
So, 6 / (2x1) = 3.

We get the same value, but we've used a method that will save us a great deal of time and headache on larger problems. Imagine writing out the combinations of 12 jurors!

2. Independent event probability
Let's again look at a very simple example. Imagine two independent events. You flip a coin each morning. And, it's either sunny or not each morning. Each event is independent on the other. Basically, we're just saying one does not influence the other.

So, we know the probability on 1 flip of obtaining heads is 1/2 (50%). And let's say we're told that the probability of a sunny day is 1/2 (50%). What is the probability that it is sunny on a day we flip a coin and get heads?

c = coin flip heads, s = sunny morning weather
P(c) x P(s) = P(c+s)
1/2 x 1/2 = 1/4.

Obviously, this is an easy example. But, more challenging examples are posted frequently to the board.

ok, thank you.. 2 down about 4 to go.

I have meetings most of the morning, but I'll post more as I can.

Remember, #1 answers your #6 as well (since they are the same thing).

#4 and #8 (as they are related)

First, you need to understand union and intersection. If you have a set of values A and a set of values B, you can represent their combined value as a union AUB.
AUB = A + B - AB
We subtract AB because we don't want to count their overlap of values twice. See image (aub.gif).

We can represent their intersecting values (where both A and B have value) as A"I"B ("I" in normally shown as an upside-down U).

AIB = AB
Basically, we just want their overlap area. See image (aintb.gif).

On the GMAT, I believe you'll encounter these types of problems as probability events. For example, you will be given the probability of a certain event, the probability of another event, and the probability of both events, and you'll be asked to find the probability of either happening.

P(A or B) is basically asking for AUB. What is the probability of EITHER A or B.

P(A and B) is basically asking for AIB. What is the probability of BOTH A and B.

I'll try to give any example...
The probability of an earthquake on any given day in LA is 10%. The probability of smog on any given day in LA is 40%. If the probability of an earthquake and smog on any given day is 5%, what is the probability of LA suffering from smog or an earthquake on any given day.

A = Earthquake
B = Smog

They are asking for P(A or B).
By our formula above, P(A or B) =
P(A) + P(B) - P(AIB)
10% + 40% - 5%
1/10 + 4/10 - 1/20
2/20 + 8/20 - 1/20
9/20

So, P(A or B) = 9/20 or 45%.


Another example...
The probability of either smog or an earthquake in LA on any given day is 45%. The probability of smog on any given day is 40%. The probability of an earthquake on any given day is 10%. What is the probability of both smog and an earthquake occuring on the same day?

P(A or B) = P (A) + P (B) - P(AIB)
45% = 40% + 10% - P(AIB)
9/20 = 4/10 + 1/10 - P(AIB)
9/20 - 5/10 = - P(AIB)
9/20 - 10/20 = - P(AIB)
-1/20 = - P(AIB)
P(AIB) = 1/20 = 5%.

Obviously, the GMAT problems are more challenging.

Thats great, thanks so much.. all i need is a simple example like that because I was just getting confused on which types of questions required a specific formula.. Thanks again its greatly appreciated.