The number of ways in which four different toys and five indistinguishable marbles can be distributed between 3 boys, if each boy receives at least one toy and at least one marble, is

Step-by-step solution

5 identical marbles can be distributed to 3 boys, each receiving at least one in 5 - 1 C 3 - 1 = C 4 2 ways 4 different toys can be grouped as 2 , 1 , 1 in 4 ! 2 ! 1 ! 1 ! = 4 ! 2 ! ways Two boys will get 1 each and they can be selected in C 2 3 ways. Required number of ways = C 4 2 × 4 ! 2 ! × C 3 2 = 6 × 12 × 3 = 216