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Math Formulas for MBA

http://mathworld.wolfram.com/
Formulas for area for traiangle:

#1 Area of a traingle of side a, b, c lengths:
sqrt(s(s-a)(s-b)(s-c)) where s = 1/2(a+b+c) ie. 1/2 perimeter of the traingle

#2 Area of an isosceles triangle with equals sides of length a = root(3)/4 * a

#3 Area of a triangle of base b, height h = 1/2 * b * h

Probability Question:

Imagine a parking lot with 500 cars with license plates numbered from 001 to 500 and no two cars having the same license plate number. At 6 pm, they all leave the lot one by one. What is the probability that the license plate numbers of the first four cars to leave are in increasing order of magintude?

1/8
1/24
1/64
1/128

I am quoting a legend here :

Any four cars have an equal chance of leaving the lot first, so we can concentrate on just one specific bunch of four cars. (Whether there are 999 or just 4 cars in the lot is irrelevant). For a given set of four cars, they can leave the lot in 4! or 24 ways, only one of which the license plate numbers will be in increasing order. Hence, the answer is 1/24.

In how many ways can 4 groups of 2 each be selected from a group of 8 students?
1. 1980
2. 2520
3. 3050
4. 3670
5. 3980

[2] 2520 is the correct answer. good work.

I quote the legend akamai here:

Selecting multiple groups is EXACTLY the same as selecting one group. Let's say you are selecting 2 people from a group of 8. You are actually selected one group of 2 and one group of 6 (Which is an intuitive way of proving why 8C2 = 8C6). In the denominator of combinations with multiple groups, simply put the factorials of the number of people in each group.

2C8 = choose 2 to be IN and choosing 6 to be OUT or 8!/(2!6!)

To choose 4 groups of 2 from 8, the formula is simply 8!/(2!2!2!2!)

If you think of combinations as "adjusted" permutations, we have 8! ways to arrange 8 people, but each of the 4 pairs is an equivalent combination so we need to divide by 2^4.

General equation for circle is : (x-x1)^2 + (y-y1)^2 = r^2 where (x,y) and (x1,y1) are two coordinates.