Understanding Permutations: Definition, History, and Examples, Slides of Mathematics

Download Understanding Permutations: Definition, History, and Examples and more Slides Mathematics in PDF only on Docsity! Permutations By: Arush Gupta What is a Permutation? A permutation is an arrangement, or listing, of objects in which the order is important. Permutation is used when we are counting without replacement and the order matters. Factorial In math the explanation mark means factorial. An example is 3! = 3x2x1=6 Also the value of 0! is 1 5!= 5 x 4 x 3 x 2 x 1=120 6!= 6 x 5 x 4 x 3 x 2 x 1=720 Examples 1. How many ways can you group F, J, and X? Answer: f, j, x- f, x, j- x, f, j- x, j ,f- j, x, f- j, f, x. 2. If you have person A, B, and C and seat 1, 2, and 3, how many ways can the people sit in the chairs? Answer: 3!= 3x2x1=6 different ways because 3 people can sit in seat 1, 2 people can sit in seat 2, and 1 person can sit in seat 3. 3. Ms. Rosa has 3 shirts, 2 skirts, and 5 pairs of shoes. In how many ways can she select 1 shirt, 1 skirt, and one pair of shoes? Answer: 3 x 2=6 x 5=30 different ways. Trivia Time!!! 1. What is the answer for 5 factorial? 2. True or False: the order matters in permutations. 3. How many different ways can you group A, B, C, and D- SHOW ALL WORK! 4. What is the answer for 8 factorial? 5. True or False: there are 3 ways to put a, b, c- explain your reasoning/show your work 6. If you have person A, B, C, D, E, and F, and you have seat 1, 2, 3, and 4, how many ways can the people sit in the seats? 7. Jacob has 5 shirts, 6 pants, and 4 jackets. In how many ways can he select 1 shirt, 1 pant, and 1 jacket? SHOW ALL WORK!!! 8. The courthouse flies the city, state and country flags. How many ways can the flags be arranged on the flag time?