The number of distinct terms in the expansion of $$(X + Y + Z + W)^{30}$$ are:

All the terms of the expansion $$(X + Y + Z + W)^{30}$$ are of the form $$k*X^a*Y^b*Z^c*W^d$$ where a,b,c,d are all positive integers and a+b+c+d=30

We need to find number of solutions of above equation and that will be the number of distinct terms in the expansion

number of solutions of equation a+b+c+d=30 is given by $$(n+r-1)C_{r-1}$$ here n = 30 and r = 4 

therefore number of solutions = $$(33)C_{3}$$ = 5456 

Therefore our answer is Option 'B'