Five racquets needs to be placed in three boxes. Each box can hold all the five racquets. In how many ways can the racquets be placed in the boxes so that no box can be empty if all racquets are different but all boxes are identical?

Hence, it is told that at least one racquet has to be there in each identical boxes, the only possibilities to arrange 5 different racquets will be : (1,1,3) or (1,2,2 ) .

Case I : (1,1,3) = Selecting 3 racquets from 5 different racquets and rest of the two goes one in each box = $$5_{C_3}$$ = 10 ways
Case II : (1,2,2) = Selecting 4 racquets from 5 different racquets and arranging them in (2,2) way in 2 identical                                             boxes  = $$5_{C_4}\times\dfrac{\ 4_{C_2}}{2}$$ = 15 ways 

Therefore, the total arrangements = 15 + 10 = 25