Subsets of fixed size 2-subsets of{I,2,3}:{I,2},{1,3},{2,3} k-uniform () ={TCS|IT=k (-( “n choose k
Subsets of fixed size 2-subsets of { 1, 2, 3 }: {1, 2}, {1, 3}, {2, 3} S k ⇥ k-uniform = {T S | |T| = k} “n choose k” ✓n k ◆ = ✓[n] k ◆
Subsets of fixed size n(m-1)…(m-k+1) n! k(k-1)·1 k!(n-k)！ of ordered k-subsets:n(n-1)...(n-+1) of permutations of a k-set:(-1)...1
Subsets of fixed size n k ⇥ = n(n 1)···(n k + 1) k(k 1)··· 1 = n! k!(n k)! # of ordered k-subsets: n(n 1)···(n k + 1) # of permutations of a k-set: k(k 1)··· 1
Binomial coefficients Binomial coefficient: n! k k!(n-k)月 m choose a k-subset台 n-k choose its compliment 2. 0-subsets I-subsets +.. k k=0 n-subsets all subsets
Binomial coefficients Binomial coefficient: n k ⇥ n k ⇥ = n! k!(n k)! 1. n k ⇥ = n n k ⇥ 2. ⇤ n k=0 n k ⇥ = 2n choose a k-subset 㱻 choose its compliment 0-subsets + 1-subsets + ... + n-subsets = all subsets