which answer is right and why?

We choose 450 people to form a club from 800 applicants. Among these 800 people, 360 have money. 320 have time, and 160 have both. Of those who have money, 30 were not admitted to the club. Of those who have time, 60 were not admitted to the club. Of those who have both, 150 were granted admission to the club. 350 of the applicants were denied admission to the club.

Find the probability that an applicant who do not have either time nor money and was still admitted to the club.

 

Solution 1: The set of people who  have  time and/or money has a total of 520 people. (680 - 160 = 520).  Out of these people, 80 people didn't make it into the club (30+60-10). Therefore, 440 people who have time/money made it into the club.

 

800 - 520= 280 people who do not have time/money. Out of these people, 270 people did not get into the club because 350-80=270. That means 10 people out of the 280 people who do not have time/money got into the club. The probability is 1/28.

Solution 2: "Of those who have money, 30 were not admitted to the club. Of those who have time, 60 were not admitted to the club. Of those who have both, 150 were granted admission to the club."  These statements mean it rejected 80 people who had either time/money or both. (10 people have both. 50 have time. 20 have money). Among the number 360+320-80=600, there are 150 have both and they are counted twice. So the people in the club who has time or money, or both is 600-150=450. There are 450 got into the club. So the answer is 0.

 

I think the solution 1 is wrong. Why?