for the birthday problem, the probability that at least 2 people out of N total share the same birthday is 1-365*364*....*(365-N+1)/365^Nwhat would be the probability that at least k people out of N total (k<N) share the same birthday (any date)?what about the probability that at least k people out of N total (k<N) share a specified birthday (a pre-determined fixed date)?

For the first one use inclusion-exclusion principle; for the second just do 1 - P(nobody is born on specified date) - P(1 person bought that date)-...-P(k-1 people born on that date), each of the terms is easy to calculate.I am not sure if the answers simplify.

QuoteOriginally posted by: kolombofor the birthday problem, the probability that at least 2 people out of N total share the same birthday is 1-365*364*....*(365-N+1)/365^Nwhat would be the probability that at least k people out of N total (k<N) share the same birthday (any date)?what about the probability that at least k people out of N total (k<N) share a specified birthday (a pre-determined fixed date)?there exists other approach for k = 2 to construct a solution. The number of favourable events is a permutation of N taking k at a time. The total number of outcomes are 365^N

QuoteOriginally posted by: listQuoteOriginally posted by: kolombofor the birthday problem, the probability that at least 2 people out of N total share the same birthday is 1-365*364*....*(365-N+1)/365^Nwhat would be the probability that at least k people out of N total (k<N) share the same birthday (any date)?what about the probability that at least k people out of N total (k<N) share a specified birthday (a pre-determined fixed date)?there exists other approach for k = 2 to construct a solution. The number of favourable events is a permutation of N taking k at a time. The total number of outcomes are 365^NSorry, i lost the factor 365 in the numerator.