In how many ways can 5 rings be worn on the four fingers of the right hand?
this is a complete question!
this is a complete question!
Okay so you have 5 rings A B C D and E
For the first finger how many options do you have ?
5
After that you have 4 rings to choose for the third finger...and so on
5x4x3x2 = 120 different ways.
But you can actually choose 5C4 = 5 different sets if rings
ABCD
ABCE
ABDE
ACDE
BCDE
But within each set of 4 letters we can sort them
4x3x2x1 = 24 ways
And this is why 24x5 = 120
Lets dig even more:
ABCD
Well you can start with with a letter and sort the rest of it:
For example A
A BCD
A BDC
A CBD
A CDB
A DBC
A DCB
so if you realized now we kept one letter and played with the three others
BCD = 3x2x1= 6 ways
Since we have 4 letters
4x6 =24
This is the basic idea of factorials.
5! = 5x4x3x2x1
