Three gentlemen and three ladies are candidates for two vacancies.A voter has to vote for two candidates.In how many ways can on cast his vote?

Question

Three gentlemen and three ladies are candidates for two vacancies.A voter has to vote for two candidates.In how many ways can on cast his vote ?

I used combination to solve this question using C$(6,2)$.
But according to relation of permutation and combination$\displaystyle\frac{C(n,r)}{r!}=P(n,r)$.I could solve using permutation as $\displaystyle\frac{P(6,2)}{2!}$.
I want to know what does $\displaystyle\frac{P(6,2)}{2!}$ it mean in logical terms(E.g Arrangement of 6 persons among 2 vacancies,but I couldn't digest use of 2! in this equation )

Please tell me use of 2! in this question in logical terms.

Answer 1

I got this answer from @lulu
It must be divided by $2!$ because these two posts are identical(E.g (a,b)=(b,a))