All the terms of the expansion (X+Y+Z)30 are of the form k×Xa×Yb×Zc×Wd 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)Cr−1 here n=30 and r=4 therefore number of solutions =33C3=5456 Therefore our answer is Option 'B'