need to clear this simple counting concept

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

logitech wrote: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.

I think your answer is incorrect, check this post
https://www.beatthegmat.com/difficult-ma ... ght%20hand

hope what is in the post is correct. a similar problem well discussed here.
https://www.beatthegmat.com/p-c-problem- ... %20%20ways