Problem Solving

Question # 35
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?

A) 0

B) 27

C) 30

D) 99

E) 78


Therefore, the number who played at least one sport = the number in Baseball + the number in Basketball + the number in Soccer - number who played exactly two sports -2 *(the number who played all three sports) = 66 + 45 + 42 - 27 - (2 times 3) = 153 - 27- 6 = 120. Since 120 of the students played at least one sport, 150 - 120 = 30 played none of the sports.
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But why is the P(A U B U C) = P(A) + P(B) + P(C) - P(A^B) - P(B^C) - P(C^A) + P(A^B^C) formula not used here.

Pls explain