Answer
10626 ways
Work Step by Step
Let p,q,r,s,t be the number of pennies, nickels,
dimes, quarters, and half dollars respectively.
We know p$\geq$0;q$\geq$0;r$\geq$0;s$\geq$0;t$\geq$0
and p+q+r+s+t = 20.
Number of ways is given by $C$(n+r-1,r)
here n=5 r=20
So $C$(24,20) = 10626 ways