In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
Choose the correct choice from the following answers:	A) 20	B) 30	C) 25	D) 600	E) None of these
The toys are different; The boxes are identical.   If none of the boxes is to remain empty, then we can pack the toys in one of the following ways:   Case i. 2, 2, 1   Case ii. 3, 1, 1   Case i:   Number of ways of achieving the first option 2, 2, 1.   Two toys out of the 5 can be selected in 5C2 ways. Another 2 out of the remaining 3 can be selected in 3C2 ways and the last toy can be selected in 1C1 way.   However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2.   Therefore, total number of ways of achieving the 2, 2, 1 option is:25
<result>C</result>
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?