Theorem(Sum Principle) SnT=0→ISUT=1S1+1T到 4口·1①，43，t夏，里)Q0 Hengfeng Wei (hfweixinju.edu.cn) 2-3 Counting March12,20209/34
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theorem (Sum Principle) S ∩ T = ∅ =⇒ |S ∪ T| = |S| + |T| Theorem (Product Principle) |S × T| = |S| × |T| Holds for finite sets S and T. Hengfeng Wei (hfwei@nju.edu.cn) 2-3 Counting March 12, 2020 9 / 34
Theorem(Sum Principle) SnT=0→ISUT川=lS1+T Theorem (Product Principle) IS×TI=IS×T 4口·1①，43，t夏，里)Q0 Hengfeng Wei (hfweixinju.edu.cn) 2-3 Counting March12,20209/34
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theorem (Sum Principle) S ∩ T = ∅ =⇒ |S ∪ T| = |S| + |T| Theorem (Product Principle) |S × T| = |S| × |T| Holds for finite sets S and T. Hengfeng Wei (hfwei@nju.edu.cn) 2-3 Counting March 12, 2020 9 / 34
Theorem(Sum Principle) SnT=0→ISUT=S1+1T Theorem (Product Principle) IS×T=IS×T Holds for finite sets S and T. 4口·1①，43，t夏，里)Q0 Hengfeng Wei (hfweixinju.edu.cn) 2-3 Counting March12,20209/34
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theorem (Sum Principle) S ∩ T = ∅ =⇒ |S ∪ T| = |S| + |T| Theorem (Product Principle) |S × T| = |S| × |T| Holds for finite sets S and T. Hengfeng Wei (hfwei@nju.edu.cn) 2-3 Counting March 12, 2020 9 / 34
先学习下加法，1+1，就是 +- 所以1+1=2，这很好理解 那我们趁热打铁学习下一个重要公式吧： EwEw(-1)det(w)w(ex+) ePΠa>o(1-e-a) 4口·￥①，43，t豆，3)Q0 Hengfeng Wei (hfweixinju.edu.cn) 2-3 Counting March12,2020.10/34
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hengfeng Wei (hfwei@nju.edu.cn) 2-3 Counting March 12, 2020 10 / 34
Counting 4口·￥①，43，t夏，3)Q0 Hengfeng Wei (hfweixinju.edu.cn) 2-3 Counting March12,202011/34
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tuples permutations combinations Counting compositions set partitions integer partitions Counting # of functions under (twelve) different restrictions Hengfeng Wei (hfwei@nju.edu.cn) 2-3 Counting March 12, 2020 11 / 34