Question

There is a group of 265 persons who like

either singing or dancing or painting. In

this group 200 like singing, 110 like

dancing and 55 like painting. If 60

persons like both singing and dancing, 30

like both singing and painting and 10 like

all three activities, then the number of

persons who like only dancing and

painting.​

Answer 1

Answer:

Step-by-step explanation:

Let the number of people who like singing be n (S) = 200, who like dancing is n (D) = 110, number of people who like painting = n (P) = 55.

n (D ∪ P ∪ S) = 265

The number of people who like both singing and dancing = n (S ∩ D) = 60

The number of people who like both singing and painting = n (S ∩ P) = 30 and

The number of people who like all the 3 activities = n (D ∩ P ∩ S) = 10

n (D ∪ P ∪ S) = n (D) + n (P) + n (S) − n (D ∩ P) − n (P ∩ S) − n (S ∩ D) + n (D ∩ P ∩ S)

265 = 110 + 55 + 200 − n (D ∩ P) − 30 − 60 + 10

265 = 285 − n (D ∩ P)

n (D ∩ P) = 20

The number of persons who like dancing and painting = n (D ∩ P) − n (D ∩ P ∩ S)

= 20 − 10

= 10