You have three toys, and there are 4 boys and six girls. If you want to give all the toys away, and you want at least two boys to receive a toy, how many ways can this be done.

I'm not sure if I did this correctly, but I took the number of permutations possible $\displaystyle 10*9*8$, then I subtracted the number of permutations wherein two boys cannot receive a gift $\displaystyle 7*6*5$. This would become: $\displaystyle 720-210=510$.

I'm not really sure if what did was right, if my answer is correct, or whether or not there's another way of solving this. Can I ask for help?

Thanks in advance.