Question

The Venn diagram below choices of subject by 40 student.18 chose chemistry ,20 chose physics and 15 chose biology ,2 chose chemistry only,8 chose physics only and 1 chose biology only, 4 chose all students.find the number of students who chose none of the three students.​

Answer 1

10

Explanation:

Given that:

Let :

C = chemistry

B = biology

P = physics

n(C) = 18

n(P) = 20

n(B) = 15

C only = 2

P only = 8

B only = 1

All 3 subjects = 4

P n B only = 20 - (8 + x + 4) = 8 - x

C n B only = 18 - (2 + x + 4) = 12 - x

B = (12 - x) + 4 + 1 + (8 - x) = 15

B = 25 - 2x = 15

B = 10= 2x

x = 5

PnC only, x = 5

Number who chose none of the 3 subjects, k equals :

2 + x + 8 + 4 + 1 + (8 - x) + (12 - x) + n = 40

35 - 3x + n = 40

x = 5

35 - 15 + y = 40

20 + n = 40

n = 40 - 20

n = 10