Gauss Method
1 + 2 + ... + 9 + 10 = ?
55
Emma lives in Vancouver and is planning to go to Toronto via Calgary. If there are 4 flights from Vancouver to Calgary and 3 flights from Calgary to Toronto, how many different routes are there?
12
Represent 67 * 66 * 65 * ... * 2 * 1 using factorial notation.
67!
The different ways to arrange a set of items, where order matters.
Vancouver Stadium has 5 gates. In how many ways can you enter the stadium and leave the stadium by a different gate?
20
1 + 2 + 3 + 4 + ... + 98 + 99 + 100 = ?
5050
Peter bought 6 house numbers at his lumber supply store. The numbers are: 1, 2, 3, 4, 5, and 6. How many different 4-digit house numbers can you form using these numbers, if no number is used more than once?
360
Calculate 5!
120
(5 * 4 * 3 * 2 * 1)
Calculate 7P4
In how many ways can 6 different books be arranged on a bookshelf?
720
The person who created the Gauss method.
Who is Carl Friedrich Gauss?
Leo has 8 different math books, and he wishes to choose 4 of them to display on a bookshelf. How many possible arrangements are there?
1680
Calculate 5!/3!
(5! divided by 3!)
20
A swimming coach must select 4 out of 6 team members to swim at Nationals.
How many unique ways are there to arrange these swimmers?
360
Calculate 16 + 18 + 20 + 22 + 24 + 26 + 28 +30
184
When Yunji added up all the numbers from 1 to 9, she mistakenly left out a number. Her sun was 36. What number did she leave out?
(adapted from 2024 AMC 8 problem 4)
9
Students A, B, C, D, and E are to sit in a row of 5 chairs. How many ways (different orders) could they be seated if A cannot sit in the first seat?
96
Calculate 6! - 2!
718
nPr can be represented as...
n!/(n-r)!
Ava and Bob invited four other students to sit on their bench. In how many ways can these six students be seated if Ava is seated at the left end and Bob is seated at the righ end?
24
The formula for the Gauss method.
In how many ways can 5 different women and 4 different men be seated on a bench if the men and women must alternate seats?
2880
What is 0!
1
(there's one way to arrange 0 objects)
In the land of Permute-nation, combination locks are known as ‘permutation locks’. Each permutation lock requires a 6-digit code. How many possible codes are there, if each digit is distinct and no codes contain the digit 0?
60,480
In how many ways can a student council chair, a vice-chair, and a secretary be selected from the 100 students comprising the student council?
970,200