Question

Out of a total of 130 students, 60 are wearing hats to class, 51 are wearing scarves and 30 are wearing both hats & scarves. Of the 54 students who are wearing sweaters, 26 are wearing hats, 21 are wearing scarves and 12 are wearing both hats and scarves. Everyone wearing neither hat, nor a scarf is wearing gloves.
a. How many students are wearing gloves?
b. How many students not wearing sweater are wearing neither hat nor a scarf?

Answer 1

so, 49 students are wearing gloves.

16 students wearing hats but not scarves and sweaters.

Given:

Total Students is 130 , 60 are wearing hats

there 51 are wearing scarves and 30 are wearing both hats & scarves.

And 54 students who are wearing sweaters, 26 are wearing hats, 21 are wearing scarves and 12 are wearing both hats and scarves.

To find:

students are wearing gloves and students not wearing sweater are wearing neither hat nor a scarf.

Solution:

All students wearing hats or scarves are wearing gloves.

 n(H∪S) =n(H)+n(S)−n(H∩S)

 = 60+51-30

 =81

so,  n(H' n S') = 130-81 = 49

 49 students are wearing gloves.

 a) 26 students wear hat and sweater, 60 - 26 = 34 students only wear hat but not scarf.

 

If 12 students wear hats, sweaters and scarves together.

 

So, then 30-12=18 students wear sweaters and scarves.

 

So, the number of students wearing hats but not scarves and sweaters is  ( 34-18 ) = 16

so, 49 students are wearing gloves.

16 students wearing hats but not scarves and sweaters.

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