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.
HINT: Please do tell about your approach next time.

Use exclusion:

$P[$ atleast $2$ people have birthday in same month$ ]= 1-P[$no two people have birthday on same month$]$
$= 1-\frac{12.11.10.9.8.7.6}{12^7}=0.88$
$1 - \frac{{}_{12}P_7}{12^7} = 0.888599537 $

12: months 

P: permutation 

7: people 

Cheers