Every student is given a student ID number. If each number is 6 digits long, how many possible numbers are there?
Mathematics · High School · Tue Nov 03 2020
Answered on
In order to find how many possible numbers are there from a 6 digit number, we will the fractional function called factorial, denoted as “!”
Factorial is used look at permutations and combinations. Permutations tell us how many different ways we can arrange things if their order matters. Combinations tells us how many ways we can choose k item from n items if their order does not matter.
How does factorial works?
Example:
3!
= 3 x 2 x 1
= 6
4!
= 4 x 3 x 2 x 1
= 24
Simply multiply the number with n, then n-1, then n-2, until it reaches 1.
Now given that we need to calculate the possibility from a 6 digit number, it can represented as,
=6!
= 6 x 5 x 4 x 3 x 2 x 1
= 720
There are 720 possible numbers