Counting question

Because the box is indistinguishable, we can use the reccurence relation. $B(n,k)=B(n−1,k−1)+kB(n−1,k)$with $B(n,1)=1B(n,1)=1$ and $B(n,n)=1B(n,n)=1$. For your case, you need the sum $B(4,1)+B(4,2)+B(4,3)$. I trust you can use the formula to complete the problem.

HINT: There are 4 balls and 3 boxes, where all the balls are different. One of the 3 boxes has to have 2 balls.