Question 476308
you calculated the answer correctly.
n is equal to 7 or n is equal to 2.
that takes care of part a.
both of those values of n will make the equations equal.
that was confirmed.
part b says n cannot be equal to, or must be different from ... integers?
not sure i understand that, but, if i must pick a number that should be disallowed, it would be n = 2.
your equation is:
4*nC2 = (n+2)C3
this equation can be translated to:
(4*n!)/(2!(n-2)!) = (n+2)!/(3!(n+2-3)!) which becomes:
(4*n!)/(2!(n-2)!) = (n+2)!/(3!(n-1)!)
when n = 7, this equation becomes:
4*7!/(2!*5!) = 9!/(3!*6!)
when n = 2, this equation becomes:
4*2!/(2!*0!) = 4!/(3!*1!)
the left side of this equation have n equal to 2 which is equal to the number of positions in the subgroup you are trying to create.
if that's what they're referring to, then n = 2 would be disallowed because the subgroup is the same size as the group.
outside of that I'm not exactly sure what their complaint is.
assuming i understood correctly, i would say that n = 2 would be disallowed because the group created is the same size as the subgroup that would be created from it.