Balls and Boxes – Combinatorics This is studying for my final, not homework.
Six balls are dropped at random into ten boxes. What is the probability that no box will contain two or more balls?
So I know that to select 6 balls from ten we do: ${10\choose 6}$, but I'm not sure how to check whether or not each box contains less than two balls.  Is it just:
${6\choose 1}\over{10\choose 6}$

Drop a ball into a box. Now drop the next ball. There are $9$ empty boxes, so the probability of no collision is $\frac{9}{10}$. Then drop the next one. The probability of no collision is $\frac{8}{10}$. And so on.
So the overall probability of no collision is
$$\frac{9}{10}\cdot\frac{8}{10}\cdot\frac{7}{10}\cdot\frac{6}{10}\cdot\frac{5}{10}.$$
