In an examination, the maximum marks for each of three subjects is n and that for the fourth subject is 2n. The number of ways in which candidates can get 3n marks is
Total marks = Marks for first 3 papers + Marks for fourth paper =3n+2n=5n Candidate needs to get 3n marks. Let x1,x2,x3,x4 be the marks of candidate in I, II, III and IV paper, respectively. Then, x1+˙x2+x3+x4 =3n(0≤x1,x2,x3,≤n‌ and ‌0≤x4≤2n) Using multinomial theorem, Number of ways = Coefficient of x3n in ‌