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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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2 Answers 2

HINT: Please do tell about your approach next time.

Use exclusion:

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

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

12: months

P: permutation

7: people


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