12 identical blackboards are distributed among 5 schools. Find the probability that the first school receives 2 blackboards and each of the other 4 schools has to receive at least 1 blackboard. Solution total no of ways of distributin 12 identical objects among 5 peolpe is (12+5-1)C12= 16C12. also after giving 2 blackboard to 1st school and giving 1 each to the left four schools we are left with 6 blackboards. now these 6 blackboards are to be distributed among the rest 4 schools. so number of ways of doing this is (6+4-1)C6=9C6. so the prob is 9C6/16C12.