I am have trouble with this probability question?

Question

this is what it says 'a musli bar company has a current promotion where they place placing cars in each box. there are 12 different cars altogether how many ceral boxes would you need to buy in order to obtain all 12 cars' please can anyone help this seems im possible to me

Answer 1

well seems like using expected values is way to go

for first car only one draw is needed

for second car expected number of draws to get a different car from first one is 1/(11/12) = 12/11

now follow this idea to get number of draws for each nth car (from first to 12th ) and then add them up

1+12/11+12/10+12/9+12/8+12/7+

12/6+12/5+12/4+12/3+12/2+12/1 = 37.238

so it will take slightly over 37 draws to get all 12 cars

hope this helps