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