You have to answer 2 essay questions for an exam. There are four essays to choose from. How many different groups of two essays could you possibly choose?

Answer 1

Based on the question, we have the situation of "4 choose 2". Since this problem is reasonable to write out we will do this first...

Assume Essay1 = A, Essay2 = B, Essay3 = C, and Essay4 = D ( to make the writing simpler )....

What groups of two essays without duplication can be found? Let's write them out... We also know that A,b is the same as B,A (they are the same two essay regardless of selection order)

1) A,B

2) A,C

3) A,D

4) B,C

5) B,D

6) C,D

So we have six possibilities of selecting two distinct essays from 4 essays. This can also be cast into the number of permutations of 4-choose-2 (this is to say without replacement/duplication)

Usually on your calculator this is represented as _nP_r due to the factorial function used [n! = n * (n-1) * (n-2) * ... * 2 * 1]

_nP_r = n! / (r! * (n-r)! ) --> 4P2 = 4! / (2! * (4-2)!) = 24/(2 * 2) = 24/4 = 6