Puzzle on Line and Angle - What are the chances that at least two out of a group of fifty people

Question:  What are the chances that at least two out of a group of fifty people share the same birthday?

Answer:
The probability of at least two out of a group of 50 people share the same birthday is 97%

Solution:
Probability of at least two share the same birthday = 1 - probability of all 50 have different birthdays

Probability of all 50 have different birthday
= 365/365 * 364/365 * 363/365 * ... * 317/365 * 316/365
= (365 * 364 * 363 * 362 * ... * 317 * 316)/36550
= 0.0296264

Probability of at least two share the same birthday
= 1 - 0.0296264
= 0.9703735
= 97% approx.

Thus, the probability of at least two out of a group of 50 people share the same birthday is 97%.