http://www.collegeboard.com/student/testing/clep/ex_cm.html

http://esc.pec.ngb.army.mil/studentguide/pas.cfm

http://www.freeuniv.com/lect/mathpage.html

SAT Test Prep

http://dept.owc.edu/resources/subject.html

the number of ways to arrange books on a shelf, this is permutations.

if you have 4 books then there are 24 ways to arrange them which is written as 4!.

if you have n objects there are n! permutations.

3! means 3*2*1, 4! = 4*3*2*1, 0! = 1 be definition and 1! = 1.

n! = n*(n-1)(n-2)….2*1*0! for any positive integer n.

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if you roll a fair die twice you can get one even and one odd number, two odd or two even numbers. there is 1/2 chance of an even or odd on any given roll.

prob that you have two odd numbers is 1/2*1/2 = 1/4. 1/2 on each roll. this is the same prob for two even numbers

prob that you get one even and one odd would be 1/2*1/2 + 1/2*1/2 = 1/2. this is the prob of getting and even then odd plus the prob of getting and odd then an even.

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for the number of draws to get a black card depends on the method for drawing. is it with replacement or not?

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i think the last part, sub(a) C sub(b) is just a short hand way of saying a choose b which means how many ways you can choose b objects from a objects. the formula is a!(b!(a-b)!)

so here a>=b and both a and b are integers. look at combinations for more info.