Question

take any drinks, isThe school organised a larewell party of 100students and school management decidedtree types of danks distnbutes in party areM Coffee C) and Tea T) Hereported the following to students hadthe three drinks MCT. 20 had V and 30bad and T. 25 had M and T 12 hadonly: 5 had C only: Bhad T onlyii) The number of students who prefer Milkam) The number of students who preferCoffee isbi sodi 50(iv) The number of student who preler Teaistal 57d) 17[v] The number of students who prefer Nand Collee but not tea istel 15 20Add File​

Answer 1

Given:

• the school organized a farewell party of 100 students.
• three types of drinks were distributed at the party that is milk, tea and coffee.

To find:

• The number of students who prefer tea?
• The number of students who prefer coffee?
• The number of students who prefer milk?
• The number of students who prefer milk and coffee but not tea?

explanation:

consider the following venn diagram,

a = Number of students who had M only

b = Number of students who had M and C Only

c = Number of students who had C only

d = Number of students who had 7 only

e = Number of students who had M and 7 only f = Number of students who had three drinks M, C. T and

g = Number of students who had C and 7 only.

Then we have,

                     a=12, b+1=20, c=5,d=8, e+f=25, f = 10, g + f = 30

                    = a=12, b=10, c=5, d=8, e=15, t=10 and g=20

Now,

The number of students who prefer Milk and Coffee but not Tea is,

                                           i.e. b = 10

The number of students who prefer Coffee,

                                            = b+c+f+g

                                            = 10+5+10+20

                                            = 45

The Number of students who prefer Milk,

                                            = a+b+f+e

                                            = 12+10+10+15

                                            =47

The number of students who prefer coffee,

                                            = b+c+f+g

                                            = 10+5+10+20

                                            = 45.

The venn diagram is attached to this answer.