Hello, perash!

This is a classic . . . The Birthday Paradox.

. . I'll do the easy one.

Thirty people write down the day and month of their birth.

a) What is the probability that 2 or more of these dates will be the same ?

The opposite of "at least one match" is "nomatches."

Person #1 can have any birthday: .

#2 can have any of the remaining 364 days: .

#3 can have any of the remaining 363 days: .

. . . and so on . . .

#30 can have any of the remaining 336 days: .

Hence: .

Therefore: .

. . (I'll letyoucrank it out.)

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