birthday problem use combinatorics to answer them 1 for a group on n unrelated people that is un

1) For exactly one common birthday, we first choose 2 people out of n to have the common birthda

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Birthday Problem (Using combinatorics to answer them) 1) For a group of n unrelated people (that is, under the standard assumptions of the birthday problem), give an exact expression for the probability that there is exactly one common birthday. 2) Using the expression from [1], find the smallest value of n for which the probability of exactly one common birthday is larger than the probability of no common birthdays. Hint: When comparing the two expressions, there is a lot of cancellation. 3) Give an exact expression for the probability that there are exactly two pairs of people who have common birthdays. 4) If three people have the same birthday, we will count it as three pairs of people who have common birthdays. Give an exact expression for the probability that there are exactly three pairs of people who have common birthdays.

          Birthday Problem (Using combinatorics to answer them)
1) For a group of n unrelated people (that is, under the standard assumptions of the birthday problem), give an exact expression for the probability that there is exactly one common birthday.
2) Using the expression from [1], find the smallest value of n for which the probability of exactly one common birthday is larger than the probability of no common birthdays. Hint: When comparing the two expressions, there is a lot of cancellation.
3) Give an exact expression for the probability that there are exactly two pairs of people who have common birthdays.
4) If three people have the same birthday, we will count it as three pairs of people who have common birthdays. Give an exact expression for the probability that there are exactly three pairs of people who have common birthdays.

Added by Taylor C.

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