How many combinations will exist from a set of $5$ items; such that $\{1,2,3,4,5\}$ is one set and $\{2,4,3,5,1\}$ is another set and so on with no duplicates. I am new to this set theory and would like to learn.
Asked
Active
Viewed 451 times
1 Answers
1
The first item can be chosen in 5 ways. Since we avoid duplicates, the next item can be chosen in 4 ways, and so on. In total, there are $5\cdot 4 \cdot 3 \cdot 2 \cdot 1 = 120$ combinations.
Mankind
- 13,170
-
Thank you. I thought it will be 25 combinations. Since 5 items in a set arranged in 5 ways. – jay.mila Sep 17 '20 at 08:30
-
What is the formula you used to calculate? – jay.mila Sep 17 '20 at 08:45
-
I use the formula that says that if you want to take $n$ elements without repetitions from a set of $n$ different elements, then you can do this in $n! = n\cdot (n-1)\cdots 2\cdot 1$ ways. – Mankind Sep 17 '20 at 09:26