In a group of 270 college students, it is found that 64 like brussels sprouts, 94 like broccoli, 58 like cauliflower , 26 like both brussels sprouts and broccoli, 28 like both brusselssprouts and cauliflower , 22 like both broccoli and cauliflower , and 14 like all three vegetables.
how many of the 270 students do not like any of these vegetables?

116 students

Step-by-step explanation:

we let

U=[Total number of students ]

This implies that,

n(U)=270

B.S=[Those who like brussels sprouts ]

This implies that,

n(B.S)=64

B=[Those who like broccoli]

This implies that,

n(B)=94

C=[Those who like cauliflower]

This implies that,

n(C)=58

Using the formula :

n(U)=n(B.S)+n(B)+n(C)-n(B.S n B)-n(B.S n C)-n(B n C)+n(B.S n C n B)+n(no set)

By substitution we get,

270=64+94+58-26-28-22+14+n(no set)

270=154+n(no set)

270-154=n(no set)

n(no set)=116

Hence number of students who do not like any of the three vegetables is 116