# Problem:Finding n-stickers

#### imartinmkd

##### New Member
Hello, we ( students ) were given a very randomly homework. I say randomly because we've been solving PROBABILITY tasks and now suddenly we were given a homework that doesn't even ask us to solve probability in that one.

it goes like this..

A kid wants to collect an album with stickers. The album has n-different stickers. To get a sticker, the kid has to buy a Chocholate bar which has a randomly packed sticker with it, and it costs 15 $. How many$\$ does he has to spend to collect all the stickers in the album ?

All i know is ( i suppose ) to use (n+k-1)!/k!(n-1)! to find all the combinations of the packed stickers in the chocolate bars ( duplicates included ) ... after that im lost

#### imartinmkd

##### New Member
How many chocolate bar you need to buy

- for the 1st sticker?
- for the 2nd sticker after obtained the 1st sticker? Is it random?
- for the 3rd sticker after obtained the 1st and 2nd stickers?
- etc.

See
http://en.wikipedia.org/wiki/Coupon_collector's_problem
Hi,

1 bar goes with 1 sticker, they are undependable one of another...
for example if the album has 50 stickers you will have to buy 50 bars ( to get 50 stickers ), but the problem here is that you don't know if all the stickers are going to be different. there might be duplicates ...

#### BGM

##### TS Contributor
ya, but you have not answered my second question.

#### hlsmith

##### Omega Contributor
Can you post the question verbatim. Does it say how many stickers there are in total?

#### imartinmkd

##### New Member
Hi,
lets say u buy the first bar and u get the first sticker (randomly it doesnt have to be the 1st sticker in the album )
So , next you will have n-1 missing stickers,
Then u buy the next bar, it could either be a duplicate ( same as the first sticker u got from the previous bar,) or a different one from the first
If it is different from the previous sticker u got, then u wiill have n-2 missing stickers ..
And so on... Untill u get all the missing stickers
I did a research and found out these problems are linked with coupon collector chapter from probablity and statistics book chapter.
I stil tryin to figure out what equation i need to use ...
Any help would be appreciated
Thanks,
Martin

#### imartinmkd

##### New Member
Can you post the question verbatim. Does it say how many stickers there are in total?
Hi,

It doesn't say how many exactly.
It says there are n-stickers in the album

Tips:
But for solving i use concrete number. For example 50 (stickers) and tryin to get some results.
If its correct, i would transform the equation for n-sample

#### BGM

##### TS Contributor
Ok so if you know that the number of bars required to obtain the 2nd stick after the 1st stick is random, what is its distribution? Just figure it out. Eventually, you will know that the total number of bars (and the relevant costs) required will be a random variable. There is no equation involved in figuring out the distributions, you just merely need to describe them.