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In a group of 23 people, the probability that any 2 people share a birthday is:

1 - [tex]\frac{365!}{342!365^{23}}[/tex]

Why can't I just do the following?

[tex](23\mathbf{C}2)(\frac{1}{365})[/tex]

Thanks!

1 - [tex]\frac{365!}{342!365^{23}}[/tex]

Why can't I just do the following?

[tex](23\mathbf{C}2)(\frac{1}{365})[/tex]

Thanks!

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