Question

In a school all the student play at least one of three indore game - chess carrom table tennis . 60 play chess,50 play table tennis, 48 play carrom , 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess. Wat can be the maximum and minimum number of student in a school

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Answer 1

Answer:

maximum number of student in a school--- 123

minimum number of student in a school--- 111

Step-by-step explanation:

Let C denote  chess and C' denote carrom and T denote Table Tennis.

Let n denote the number of students in the game.

Hence,

n(C)=60

n(C')=48

n(T)=50

n(C∩T)=20

n(C'∩T)=15

n(C∩C')=12

Hence, we know the property that:

n(C∪C'∪T)=n(C)+n(C')+n(T)-n(C∩T)-n(C'∩T)-n(C∩C')+n(C∩C'∩T)

⇒ n(C∪C'∪T)=60+48+50-20-15-12+n(C∩C'∩T)

⇒ n(C∪C'∪T)=111+n(C∩C'∩T)

So, the minimum number of students are obtained when none of the students will play all of the three games and maximum number of student is obtained when  min{12,15,20}  will play all the three games.

Hence,

when n(C∩C'∩T)=0

            n(C∪C'∪T)=111  i.e. the minimum number of students are 111.

when n(C∩C'∩T)=12

            n(C∪C'∪T)=123  i.e. the maximum number of students are 123.