Question

In a class of 33

students, 20 play cricket, 25 football, and 18

volleyball, 15 play both cricket and football, 12play both

football and volleyball and 10play both cricket and volleyball.

If each student plays at least one game

How many play only cricket ?

(a) 2 (b) 4 (c) 7 (d) 8

How many play all 3 games ?

(a) 2 (b) 4 (c) 7 (d) 8​

Answer 1

Answer

(a) 2

Explanation:

(a) Total = 33 = 20 + 25 + 18 - 15 - 12 - 10 + n(All three) + 0

n (All three) = 7

Now think of the cricket circle. 20 play cricket. 15 play cricket and football (including 7 who play all three). 10 play cricket and hockey (including 7 who play all three).

So 15 + 10 - 7 (because 7 is double counted, we subtract it once) = 18 play at least one sport other than cricket too.

Therefore, only 20 - 18 = 2 play cricket only.