of 50 students, 40 are in the football team and 30are in the cricket team. how many are in both if six do not play either.

Let F be football only

FC football and cricket
C is cricket only

F+FC+C=44
and
F+FC=40
C+FC=30

put the second equation into the first
40+C=44 or Cricke only is 4
then FC is 26
and F is 14

To determine the number of students who are in both the football and cricket teams, we can use the principle of inclusion-exclusion.

First, we know that there are a total of 50 students, and six do not play either sport. So, to find the number of students who play at least one sport, we subtract these six students from the total: 50 - 6 = 44 students play at least one sport.

Next, we know that 40 students are in the football team, and 30 students are in the cricket team. However, if we just add these two numbers (40 + 30), we would be counting the students who are in both teams twice. Therefore, we need to subtract the number of students who play both sports.

Let's represent the number of students who play both football and cricket as "x". Now we can use the principle of inclusion-exclusion to find "x".

Total students who play at least one sport = students in football team + students in cricket team - students in both teams + students who play neither sport

44 = 40 + 30 - x + 6

Rearranging the equation and solving for "x":

44 = 70 - x
x = 70 - 44
x = 26

Therefore, there are 26 students who are in both the football and cricket teams.