# The queen's stamp collector boxes his stamps, n, to a box.?

The queenâ€™s stamp collector boxes his stamps, n to a box.. Each box contains m fake stamps (counterfeits). The queen suspects the collector and randomly draws 1 stamp from each of the n boxes and has them tested. What is the probability that the sample of n coins contains exactly r false ones?

n = number of boxes

m = number of counterfeits in each box

r = number of false stamps in the random sample

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It appears that you are using n for the number of boxes and for the number of stamps in each box. Was this intended?

If so then the probability that a false stamp will be selected from any box is m/n. When all the selections are put together we have a binomial situation with p = m/n. The probability of exactly r false stamps is therefore

P(x = r) = nCr*(m/n)^r*(1 - (m/n))^(n - r).