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1 - P( that none will have the same birthday.)
Choose 10 different dates for all 10 of them from 365 days in 365C10 ways
Since each birth days can range from 1 to 365 and 10 such people are there total combinations = 365^10
well, you are considering only one ordered sequence among 10! possibilities. As the students are different, one need to add the same probability 10! times. Then you'll end up with 360P10/365^10. It does not matter whether one uses C or P, but what matters is basic counting.