Binomial/Poisson (or any ) Distribution for finding out probability of me getting into a business school,plz help with my calculation.

#1
Probability of getting into a business school is 10%,I have applied to 12 business schools,what is probability that i get accepted by atleast 1 of them?
My solution as per Binomial Distribution:-
Probability of success(p)=1/10.
Probability of failure(q)=9/10.
Number of observations(n)=12.
P(X>=1)=nCx*P^x*(Q)^n-x
=1-P(X=0).
=1-[12C0*(1/10)^0*(9/10)^12-0].
= 0.97176


My solution as per Poisson distribution:-
Mean Number of acceptances=1/10
Number of observations=12
P(X>=1)=1-P(X=0)
=1-[(e^-m)*m^x]/x!]
=[(e^-1/10)*1/10^0]/0!
=0.964


(so according to above example , probability of me getting accepted in atleast one business school is 96%, is it really true,because i have onlu 10 % chance of getting accepted when i apply to only 1 school, plz explain any mistakes)