Question

In an office, every employee likes at least one of
tea , coffee and milk. The number of employees
who like only tea , only coffee, only milk and all

the three are all equal. The number of
employees who like only tea and coffee, only
coffee and milk and only tea and milk are equal
and each is equal to the number of employees
who like all three. Then, a possible value of the
number of employees in the office is????


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Answer 1

Step-by-step explanation:

Let the number people who like all the three be denoted by x.

Therefore

A∪B∪C=nA+nB+nC−n(A∩B)−n(A∩C)−n(B∩C)+A∩B∩C

=4x+4x+4x−2x−2x−2x+x

=12x−6x+x

=7x

Therefore, the total number of people is divisible by 7 which we can see that only true in the case of 77.