What Is a Factorial?
Read this topicExplanations 5
- Factorials are a shorthand for the product of all the integers from 1 to nnn. They appear as n!n!n! in which nnn is a positive integer. From a combinatorial perspective, factori…
By Anthony Jiang, Moor Xu, Victor Wang
- If you've seen combinatorics problems before, you've probably noticed that they contain many numbers with exclamation points after them. No, combinatorialists are not mobs of an…
By Freya Edholm, Andrew Machkasov, Muhammad Hamza Waseem, Anusha Rahman
- Factorial A factorial of a non-negative integer is denoted as n!n!n!, and it is the product of all positive integers less than or equal to n. The factorial looks like 4!4!4!, or…
By Sarah Walker, Victor Wang, Anusha Rahman
- (Video) INTRO TO FACTORIALS! by Mashup Math Now that we have learned in depth about probability and series, let's dive into the topic of permutations and combinations, starting …
By Trisha
- Factorials In this first lesson in Permutations & Combinations, we will learn about factorials! A factorial is a way to multiply a whole number by every positive whole number be…
By Trisha, Anusha Rahman
Problems 15
- Find the value of 11!7!6!\dfrac{11!}{7!6!}7!6!11!.
- The number 201320132013 is expressed in the form 2013=a1!a2!⋯am!b1!b2!⋯bn!2013=\frac{a_1!a_2!\cdots a_m!}{b_1!b_2!\cdots b_n!}2013=b1!b2!⋯bn!a1!a2!⋯am!, where a1≥a2≥⋯≥ama…
- Find the value of 11!8!2!\dfrac{11!}{8!2!}8!2!11!.
- What is the value of ((n−1)!)2n!(n−2)!(n−1)\dfrac{((n-1)!)^2}{n!(n-2)!(n-1)}n!(n−2)!(n−1)((n−1)!)2 ?
- Find the value of 45!43!\frac {45!}{43!}43!45! .
- 11!12!11!2{11!} \frac {12!}{11!^2}11!11!212! =
- 24⋅32⋅5⋅7=n!2^4\cdot 3^2\cdot 5\cdot 7=n!24⋅32⋅5⋅7=n! Find nnn.
- How many zeros are at the end of 125!125!125!?
- For which integers n>1n > 1n>1 is (n−1)!(n-1)!(n−1)! divisible by nnn?
- You are dealt four cards from a standard deck of 525252 playing cards. In how many ways can you get four of a kind (four 222’s or four kings, etc)? Assume that order matters.
- Solve: 6!+5!4!\frac{6!+5!}{4!}4!6!+5!
- Each table seats 121212 people, with seat positions numbered 111 through 12.12.12. Kanye and Taylor cannot sit next to or across from each other. How many ways are there to arra…
- What is the greatest value of nnn such that 5n5^n5n divides 100!100!100!?
- Which of the following is equivalent to ∏n=513n\prod\limits_{n=5}^{13}nn=5∏13n?
- What is the units digit of 9!9!9!?