Of 80 students surveyed, 35 like kabaddi, 30 like kho-kho and 25 like badminton. 12 like both kabaddi and kho-kho, 10 like both kabaddi and badminton, 8 like both kho-kho and badminton (each of these counts includes those who like all three), and 5 like all three. How many like none of the three games?

5Correct answerYour answer15Correct answerYour answer20Correct answerYour answer65Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

At least one $= 35 + 30 + 25 - 12 - 10 - 8 + 5$ .
$= 90 - 30 + 5 = 65$ .
None $= 80 - 65 = 15$ .

Worth noting

20 forgets to add back the 5 who like all three; subtracting the three pair counts removed them once too often. 65 is the number who like at least one.

Concept: Inclusion–exclusion for three sets
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsCounting with overlapping sets

Practise this chapter →

Ten questions from Venn Diagrams, at your own pace.

Explanation