# Probability 2 people have a birthday in the same month out of 7

What is the probability that 2 people in the group have a birthday in the same month out of 7 people?

I know the answers 88.85% however I want to know how to work it out using factorials instead of fractions.

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Use exclusion:

$P[$ atleast $2$ people have birthday in same month$]= 1-P[$no two people have birthday on same month$]$ $= 1-\frac{12.11.10.9.8.7.6}{12^7}=0.88$

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$1 - \frac{{}_{12}P_7}{12^7} = 0.888599537$

12: months

P: permutation

7: people

Cheers

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