Find the total number of elements that satisfy this condition..

[eddy2017]

The n and the 6 can be distributed.

 

[eddy2017]

I'm sorry. This is the first time I do this type of exercise.

 

[BigBeachBanana]

I'm sorry. This is the first time I do this type of exercise.

$$\frac{\text{n!}}{3!(n-3)!}=\frac{n(n-1)(n-2)\sout{(n-3)(n-4)(n-5)...(3)(2)(1)}}{6\sout{(n-3)(n-4)(n-5)...(3)(2)(1)}}$$I was hoping you would notice and continue the factorial expansion in the numerator and see most of the terms cancel out.
What you have left is $$\frac{n(n-1)(n-2)}{6}=20$$This is how pka derived the equation in the previous post.

 

[eddy2017]

Thank you so much for explaining patiently. As I told you my experience with factorial has only been with permutation and combination operations

 

[eddy2017]

I will study about how to find factorial of expressions with variables in it. First thing tomorrow.

 

[eddy2017]

Thanks a lot, BBB!.