Probability of having at least 1 counter of each of 5 colours

[bre5]

If I have a box that contains 1000 counters ,200 each of 5 different colours and take 20 counters from the box at random, what is the probability that I will have at least one of each colour?

What is the formula for this calculation?

Thanks

 

[stapel]

If I have a box that contains 1000 counters ,200 each of 5 different colours and take 20 counters from the box at random, what is the probability that I will have at least one of each colour?

What is the formula for this calculation?

Based on what you've been doing recently in class, what do you think might be a useful formula or starting place for this exercise?

Please be complete. Thank you!

 

[bre5]

Based on what you've been doing recently in class, what do you think might be a useful formula or starting place for this exercise?

Please be complete. Thank you!

Sorry, probably posting in the forum

Not at school, it's a work related issue. A five spindle auto lathe produces 1000 parts, so 200 off each spindle. We check a random 20 parts and I was trying to work out the probability of having at least one off each spindle. Apart from working out all the possible outcomes from 20 random samples and then then counting how many outcomes contain at least 1 from each spindle I wouldn't know where to start. Thought this might be a good place to ask.

Brian

 

[pka]

If I have a box that contains 1000 counters ,200 each of 5 different colours and take 20 counters from the box at random, what is the probability that I will have at least one of each colour?
What is the formula for this calculation?

There is no such formula. One must know how to use the inclusion/exclusion principle.

\(\displaystyle \displaystyle\sum\limits_{k = 1}^4 {{{\left( { - 1} \right)}^{k + 1}}}\dbinom{10^3 - 2k \cdot 10^2} { 20}\dbinom{ 5} { k} \)
That sum counts the number of selections in which at least one color is missing.

If you have studied multi-sets, then a different model can apply.