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1994 AMC 12 Question 19

AMC12 · 1994 AMC 12

Question 19

Label one disk “$1$,” two disks “$2$,” three disks “$3$,” $\ldots,$ 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
  1. $10$
  2. $51$
  3. $415$
  4. $451$
  5. $501$