What Are Permutations and Factorials?
Read this topicExplanations 6
- Factorials!!! A factorial is the multiplication of all of the numbers from nnn to 111 for any integer nnn. So basically n!=n⋅(n−1)⋅(n−2)⋅⋯⋅2⋅1n! = n \cdot (n-1) \cdot (n-2) \cdo…
By Tarang Saluja, Daniel Liu, Ruiran Xun
- The product of all consecutive integers from 111 to a non-negative integer nnn is known as nnn factorial, denoted (n!)(n!)(n!). This means that for any non-negative integer nnn,…
By Cindy Zhang, Ahaan Rungta, Ruiran Xun
- How many ways are there to order 666 people in a line? For simplicity, lets call these 666 people: AAA, BBB, CCC, DDD, EEE and FFF respectively. How many different people can be…
By Yan Yau Cheng, Alex Federspiel, Ruiran Xun
- What is a Permutation? A permutation of a set of distinct symbols is an arrangement of the symbols in a line in some order. Finding Permutations Given natural numbers kkk and nn…
By Vinitha Ranganeni, Alex Federspiel, Ruiran Xun
- COMBINATIONS, PERMUTATIONS, AND FACTORIALS Combinations and permutations are used in math to show the number of different ways a set of elements (numbers, objects, things, etc.)…
By Jonathan Heller, Ruiran Xun
- (Video) Permutations and Factorials (Simplifying Math) By Eric Buffington In this video, we look at a couple examples of permutations. Summary\large{\text{Summary}}Summary Facto…
By Amy Feraco
Problems 29
- You write a program to make random 666 letter words from all the letters in the alphabet. It will stop when it runs out of different possible words. Is this a permutation problem?
- Your baseball team has 202020 people on it. Every person can play every position. The team is considered different if someone is playing a different position. If we want to find…
- Ms. Ferrara wants to make a three person team out of a group of five people. Is this a permutation problem?
- You are required to make an 888 digit password using letters, numbers, and symbols %!@. No two of the digits/characters can be the same. Is this a permutation problem?
- The 2016 BHS Battle of the Bands had 111111 groups performing. In how many different orders could the bands perform?
- There are 242424 four-digit numbers that use each of the letters 1,2,3,41,2,3,41,2,3,4 exactly once. If we list all of them in numerical order, what order will be in the 17th po…
- In how many ways is it possible to seat six people at a round table if two of the six people must not sit in adjacent seats? Assume that rotations of the table are indistinguish…
- How many different four-digit numbers can be formed by rearranging the four digits in 300730073007?
- Victor has decided to rearrange his library at home. He has decided to group books by genre and arrange them alphabetically by genre, i.e. the first group on his shelf will cons…
- How many different ways can the letters in EXPII be arranged?
- The nominees for homecoming queen are about to be announced. If there are six nominees how many different ways can the six nominees be announced?
- The football team is about to take a team picture. The first row will include 555 players and the coach. If the coach must be standing on the far left of the first row, how many…
- Zachary is making his schedule for his senior year. If Zachary has 999 periods a day, not including lunch, how many ways can he order his classes if he wants his first and last …
- On a standard baseball team there are 999 batters in a line up. How many ways can the batting order be made?
- Find the total number of ways in which the following grades can be distributed among 161616 students in a history class. 444 A's 777 B's 555 C's
- In certain states the standard license plate must be made up of three letters followed by three numbers. If Sarah gets a license plate with no repeated letters or numbers, how m…
- In certain states the standard license plate must be made up of three letters followed by three numbers. If Sarah gets a license plate with no repeated letters or numbers, how m…
- How many ways can 444 chocolate bars, 999 chocolate peanut butter bars, and 333 dark chocolate bars be distributed among 161616 people?
- Find the sum of the xxx values for every permutation of equation that can come out of the waterslide.
- A hungry squirrel pops out of its home and sees 101010 piles of acorns in its vicinity. How many different ways can the squirrel travel to all 101010 piles? Assume the squirrel …
- What is the least positive integer nnn such that 777777777 divides n!n!n!.
- Zack wants to order 444 things from the McDonald's menu: burger, french fries, milkshake, and water. He doesn't want to order a milkshake right after ordering water because he t…
- Which of the following is equivalent to 6!⋅3!5!⋅2!4!⋅1!3!6! \cdot \frac{3!}{5!} \cdot \frac{2!}{4!} \cdot \frac{1!}{3!}6!⋅5!3!⋅4!2!⋅3!1!
- Which one of the following is the largest?
- In a tournament with players {x1,...,xn}\{x_1, ..., x_n\}{x1,...,xn}, a Hamiltonian path is a permutation of these players, {y1,...,yn}\{y_1, ..., y_n\}{y1,...,yn} such that…
- In a tournament with players {x1,...,xn}\{x_1, ..., x_n\}{x1,...,xn}, a Hamiltonian path is a permutation of these players, {y1,...,yn}\{y_1, ..., y_n\}{y1,...,yn} such that…
- In a tournament with players {x1,...,xn}\{x_1, ..., x_n\}{x1,...,xn}, a Hamiltonian path is a permutation of these players, {y1,...,yn}\{y_1, ..., y_n\}{y1,...,yn} such that…
- In a tournament with players {x1,...,xn}\{x_1, ..., x_n\}{x1,...,xn}, a Hamiltonian path is a permutation of these players, {y1,...,yn}\{y_1, ..., y_n\}{y1,...,yn} such that…
- Let's say we have a permutation {1,2,3,...,n}.\{1, 2, 3, ..., n\}.{1,2,3,...,n}. We say a swap of a permutation is the interchanging of any two elements of the permutation, for …