Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?

The the number of students who sign up for all three clubs = 6

Step-by-step explanation:

The total number of students in the class is given by:

Total number of students = Number of students in poetry club+Number of students in history club+Number of students in writing club-Number of students in exactly 2 clubs-2*Number of students in all the three clubs.

Based on the information we have:

Total number of students = 59

Number of students in poetry club = 22

Number of students in history club = 27

Number of students in writing club = 28

and number of students in exactly two clubs=6

Let the number of students in the three club = x

Hence, we have:

59=22+27+28-6-2x

i. e.

59=71-2x

i. e.

2x=71-59

i. e.

2x=12

i. e.

x=6

Hence, the answer is: 6