Oct 3, 2015 20:03
@anon can you explain to me the intuition behind combination formula as I am trying to look at a proof of sylow theorem that uses it
when I dealt with those stuff in high-school I always memorized the formula
The way I see permutation formula and why it works is as follows suppose we have 5 objects as A B C D and suppose we want to get 4 ways to arrange A B C D, so for a specific fixed choice for the first one the second one will have 4 choices, but for each of those 4 choices we can have 5 different ways of getting first choice, so we get 5 * 4. One can easily now use this following logic inductively to see that permutation of K object in n system is $\frac{n!}{(n - k)!}$.
now I am trying to get somewhat similiar intuition for the combination formula
