If you want to arrange 3 characters from a group of 4 characters, how many different positions can you arrange them, in this scenario, the order of the character in each position does matter.
Let say the group consists of four characters : ABCD, then below are those positions that consists of 3 characters in a group.
ABC BCD CDA DAB ACD BDC CAD DBA ADB BAC CBD DBC ACB BCA CDB DCB ADC BDA CAB DAC ABD BAD CBA DCA
The total is 24 groups.
It is lots of works if you think about the positions one by one and it is more difficult if you need to calculate a group of 6 characters, and how about 10, 30, 100 characters?
But luckily there is a formula for this type of answer, which is called the multiplicative rule : n1xn2xn3…
In the above scenario, 4x3x2 = 24!
Think like this : group n1 consists of 4 characters that will fill the 3 positions, after taken either A,B,C or D from group n1, n2 now consists of 3 characters that can fill the 3 positions, after taken 2 characters for group n1 and n2, n3 now consists of only 2 characters left, the product of these three numbers is the group that we needed to form a group of three characters, ABC, ACD, BCA…
