How do I distribute 25 gold and 259 sliver prizes other to 500 cases that 12 bottles each

Question

Company will put prizes in 500 cases ( 12 bottles to a case ) of soft drinks, but it needs a system to decide which bottles to put the winning lids on. They plan to award 25 gold prizes and 250 silver prizes and they need a fair system for distributing them among all the bottles

Answer 1

For 500 cases, being 12 bottles each, there are going to be a total of 500*12 = 6000 bottles.

 

For the gold prize, there are 25 winning bottles out of 6000 in which makes it:

 

25/6000=1/240 in which makes one winning bottle for every 240 bottles.

 

Divide 12 from 240 for the number of cases do you place the winning bottle in, which is

 

240/12 = 20 cases. Hence, place one winning bottle in every 20 cases for the gold prize.

 

Now for the silver winning prize, there are 250 winning bottles out of 6000 in which makes it:

 

250/6000=1/24 in which makes one winning bottle for the silver prize out of 24 bottles.

 

Divide 12 from 24 gives you one winning bottle for every two cases.

 

Therefore, a fair system would be to place 1 winning bottle for the gold prize in every 20 cases, and 1 winning bottle for the silver prize in every 2 cases.