Probability and combinatorics problems - picking balls and choosing postcards I am sorry for bothering you with such a trivial and easy question (in comparison to the others asked here) but I have no idea where else I could ask. These are two problems I have to solve and I just need you to check if my solution is correct.
First: I have 10 red balls and 3 blue balls. What is the probability of picking 1 red ball and 3 blue balls?
My solution: 10/13 . 3/12 . 2/11 . 1/10 = 1/286
Or should it be 10/13 . 3/12 . 3/11 . 3/10 = 9/572?
Second: They have 16 different postcards in the shop. How many possibilities do we have if we want to choose 6 different ones?
My solution: 16 . 15 . 14 . 13 . 12 . 11 = 5765760
Thanks in advance for checking my solutions

Your method for the first problem is the probability of selecting a red, followed by $3$ blues, sequentially. We have to take into account all the different ways to arrange $3$ blues and $1$ red. Note that this is a hypergeometric random variable, giving probability
$$\frac{{10 \choose 1}{3 \choose 3}}{{13 \choose 4}}\approx 0.014$$
For the second problem, your solution would be correct if ordering mattered, but it does not. Getting $123456$ is considered the same as $654321$. We have
$${16\choose6}=8008$$
