The question is as follows, 20 persons arrive in a town having 3 hotels X, Y and Z, if each person randomly choses one of these hotels then what is the probability that at least two of them go in hotel X , at least one in hotel Y and at least one in hotel Z.
2026-03-26 04:53:12.1774500792
What is the probability of chosing the hotels in the given way.
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Using compliment: $$P(S)=1-P(F)=1-[P(X=0)+P(X=1)+P(Y=0)+P(Z=0)-P(X=0,Y=0,Z=20)-P(X=0,Y=20,Z=0)-P(X=1,Y=0,Z=19)-P(X=1,Y=19,Z=0)].$$