Question

In a group of 100 students, 60 play cricket, 50 play volleyball, and 28 play both. Find the number of students who played at least one of the two games.

a) 62
b) 70
c) 78
d) 90

Answer 1

The number of students who played at least one of the two games (cricket or volleyball) is found using the principle of inclusion-exclusion and equals 82, which is not listed in the given options.

Step-by-step explanation:

To find the number of students who played at least one of the two games, we can use the principle of inclusion-exclusion. This principle states that if we want to know the total number of elements in two overlapping sets, we must add the number of elements in each set and then subtract the number of elements that are in both sets to avoid double-counting.

Let's denote the following:

C = number of students who play cricket

V = number of students who play volleyball

B = number of students who play both cricket and volleyball

The formula for the principle of inclusion-exclusion is:

At least one game = C + V - B

Substituting the given values into the formula:

At least one game = 60 (cricket) + 50 (volleyball) - 28 (both)

At least one game = 110 - 28

At least one game = 82

Therefore, the number of students who played at least one of the two games is 82, which is not listed in the given options. It seems there may have been a miscalculation or typo in the options provided.