If prizes are distinguishable-
Case 1-
(1,2,2,1)
4C2 * 6C4 * (4!)/2!2! * 2! = 1080
Case 2-
(1,1,1,3)
4C1 * 6C3 * ((3!)/3!) * 3! = 480
so, 1080+480 = 1560
If prizes are indistinguishable-
Case 1-
(1,2,2,1)
We just need to select 2 out of 4 persons who are getting 2 prizes each,cause selecting indistinguishable prizes won't make any sense as all are same hence there is only one-way,so 4C2 * 1 = 6
case 2-
(3,1,1,1)
Similarly, pick 1 person out of 4 who's getting 3 prizes = 4C3 = 4
Hence, 6+4 = 10
Or,you can apply a formula for indistinguishable-items i.e, (n-1)C(r-1) = 5C3 = 10