the logic for 7 identical things to 5 people-
1 st we have to find out all d cases-
eg(7,0,0,0,0)-5 ways
(6,1,0,0,0)- 5c2*2 ways
(5,2,0,0,0)-5c2*2ways
(5,1,1,0,0)-5c3*(3!/2) ways
(4,3,0,0,0)-5c2*2 ways
(4,2,1,0,0)-5c3*3! ways
and there are a few more cases-
it ends with (2,2,1,1,1)- 5!/(2!*3!) ways.
the sum of all the ways gives the soln.
easier way is a+b+c+d+e=7 11c4