IEN 311 Lecture 1: Permutations and Combinations 1

• School: University of Miami
• Department: Industrial Engineering
• Course: IEN 311
• Professor: Dr. Francesco Travascio

Document Summary

We can consider permutations on objects taking a few at a time. Theorem: the number of permutations for n objects taken r at a time is: npr= n!/ (n-r)! Example: our class is composed of 45 students. We want to choose 2 to bring markers to the class. The number of permutations of n objects arranged in circle is (n-1)! Example: i want to dispose in circle 4 trees in my garden. Solution: in case the objects are n=4 and they are placed in circle. The (cid:374)u(cid:373)(cid:271)er of per(cid:373)utatio(cid:374)s of (cid:374) o(cid:271)je(cid:272)ts of whi(cid:272)h (cid:374)(cid:1005) are of a ki(cid:374)d, (cid:374)(cid:1006) are of a differe(cid:374)t ki(cid:374)d . Nk are of a different kind is: n! Partitioning n objects in k cells of different size. A combination of n objects taken r at a time is a partition of n objects in two cells: one of size r and the other of size (n-r)