Whats the probability of getting 6 dots on die atleast once after throwing 10 times? Whats the probability of getting 6 dots on die atleast once after throwing 10 times?
Most logical way to solve this is to use reverse event, right? :
$A=$Getting $6$ atleast once
$A'=$Not getting $6$ at all
$$\omega=6^{10}$$
$$P(A)=1-P(A')$$
$$P=1- \left(\frac{5}{6}\right)^{10}$$

Your answer is correct. 
Since probability of getting 6 dots, $\frac16$ and that of not getting 6 dots, $\frac{5}{6}$ both remain constant from one throw to the next. Therefore, you can also use Binomial distribution to find probability of getting $6$ dots on the die, at least once in 10 throws as follows 
$$1-\text{Probability of not getting 6 dots at all in 10 throws}$$
$$=1-^{10}C_0\left(\frac{1}{6}\right)^0\left(\frac{5}{6}\right)^{10}$$
