see lets take two boys b1 & b2.
first case
6 apples are to be distributed
if b1 gets 1 apple then b2 will get 5 therefore we write (1,5)
similarly no. of cases are
(0,6);(1,5);(2,4);(3,3);(4,2);(5,1);(6,0)
therefore the total ways are 7 but we have a condition that both boys should get atleast one fruit therefore (0,6) & (6,0) are not valid
therefore total ways of distributing apples = 5
similarly total ways of distributing bananas & oranges is 7 & 10
therefore total ways = 7*5*10 = 350