Let's Party!

Probability Level 4

Mr. and Mrs. Hudson invited 40 guests to their club for a party. They were all seated in a vast hall inside the club. Outside the receptionist who was looking at the guest list was wondering how many people shared the same birthday.

What is the probability that among all the people in the hall, not one person shared his/her birthday with anyone else?

Details and Assumptions \large \text{Details and Assumptions}

  • Consider that each year has 365 days, (ignore leap years).

  • Give the answer correct to 3 decimal places.


The answer is 0.10877.

Arpit MIshra by Arpit MIshra , 21, India

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2 solutions

Archit Agrawal
Jan 21, 2017

Probability is 365C40*40!/(365)^40.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

it was a horendous job for me to enter this into wolfram alpha

Prakhar Bindal - 4 years, 4 months ago
E Koh
Oct 24, 2019

Probability that none of the 40 people share their birthday is. (365×364×363×...×326) /(365^40) ie. (365P40)/365^40 ie. 10.8768%

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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