In a group of 120 people:
65 eat Rice, 45 eat Bread, 42 eat Curd,
20 eat both Rice and Bread, 25 eat both Rice and Curd, 15 eat both Bread and Curd,
and 8 eat all three items.
Which of the following is the number of people who eat at least one of the three items?
🎥 Video solution / Text Solution of this question is given below:
Using the formula for union of three sets:
n(R ∪ B ∪ C) = n(R) + n(B) + n(C) − n(R ∩ B) − n(R ∩ C) − n(B ∩ C) + n(R ∩ B ∩ C)
Substitute:
= 65 + 45 + 42 − 20 − 25 − 15 + 8
= 152 − 60 + 8
= 100
Hence, 100 people eat at least one of the three items.