"n pick k" and "n choose k"
I am REALLY confused between "n pick k" and "n choose k". If I am not mistaken "n pick k" is n!/(n-k)! and "n choose k" is n!/k!(n-k)!, when do I use which?
LauraHYu: Jan. 24, 2015, 9:31 a.m.
"n choose k" is when you are simultaneously taking k from a set of n, k would just be a subset of n when braces are used. In the "n choose k" situation, {x, y} and {y, x} are the same so that is why I think you divide it by k! to get rid of the repeats.
LauraHYu: Jan. 24, 2015, 9:35 a.m.
"n pick k" is when you have a situation where there is a first, second, third place (you are creating order) so in this case, using parentheses instead of braces, shows that (x, y) and (y, x) are actually two different elements so you don't have to divide by k! In the ordered "n pick k" case, you should always have more possible outcomes than when you have a "n choose k" situation.
weisbart: Feb. 1, 2015, 10:59 a.m.
LauraHYu, your answer is perfect.