Question

Label one disk “1”, two disks “2”, three disks “3”, … and fifty disks “50”. Put all these labeled disks into a box. Then disks are drawn from the box at random without replacement. What is the minimum number of disks that must be drawn to guaranteedrawing at least twelve disks with the same label? Explain your reasoning.

Answer 1

we have to take worst case scenario here.

Lets take all the disks of numbers 1 to 11. which is 1+2+3+...11 = 66.

Now from the remaining disks of number 12 to 50, we can get 11 disks of each number for worst case scenario

by not taking the 12th one from any of them. There are in total (50-12+1) = 39 different numbers from 12 to 50.

So, picking 11 from every number i.e 39X11 = 429.

So total of 66 + 429 = 495 disks we can pick without picking the 12th one.

Now, if we pick anyone of the remaining disk, we will get the 12th disk.

So, we have to pick total of 496 atleast in worst case scenario to get the 12 disks of same number.