i have 6 balls .

balls 1-3 are white

balls 4,5 are red

ball 6 is blue

we throw these balls into 5 holes numerated 1-5

what is the probability that in hole number 3 we get only red balls

and there is no red balls in the other holes

i saw another student soluton and it says

$\displaystyle \frac{1^24^4}{5^6}$

cant understand the numerator

we need to choose 1 red ball out of 2 for hole number 3,so its $\displaystyle \binom{2}{1}$

divided by $\displaystyle 5^6$

am i correct?