Mathematics

Question 1

if you have the set {1,2,3,4} how many different ways can you arrange the numbers?

Answer 1

I can write this set 24 different ways, because:

4! = 4 * 3 * 2 * 1 = 24

Question 2

what is n-choose-k by mathematical definition and what does it mean?

Answer 2

(N/K) = N! / K!(N-K)!

ex) N=4; K=2

if I have a 4 element set {1,2,3,4}

I can write this set 24 different ways, because:
4! = 4 * 3 * 2 * 1 = 24

if you write them all out and take the first two numbers of each and count how many times the same set appeared (unordered) you would get:

12,13,14,23,24,34 (6 elements)

But, each time a set appeared, it appeared twice forward and twice backward. SO

(4/4) = 4! / 2! (twice forward) 2! (twice backward)

= 6 elements