1994 AHSME Problem 19

Label one disk "1", two disks "2", three disks "3", ..., fifty disks "50". Put these 1+2+3+ \cdots+50=1275 labeled disks in a box. Disks are then drawn from the box at random without replacement. The minimum number of disks that must be drawn to guarantee drawing at least ten disks with the same label is

\textbf{(A)}\ 10 \qquad\textbf{(B)}\ 51 \qquad\textbf{(C)}\ 415 \qquad\textbf{(D)}\ 451 \qquad\textbf{(E)}\ 501

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.