What have done towards working this problem?
You need to use a Venn diagram.
Please show what you can do with this.
1. Of the 190 students graduating from Statsville high school, 111 played on a sports team, 26 served on the student council, and 67 were members of clubs. Only 10 students did not participate in any of these activities. If 13 students were members of both a team and a club, 9 were on both a team and the student council, and 11 were a member of both the student council and a club, how many graduating students have been a member of a team as well as the student council and a club. Use the principle of inclusion and exclusion to solve.
Hello, William!
By the way, this problem does not involve Permutations.
There are formulas for this situation . . .1. Of the 190 students graduating from Statsville high school:
111 played on a sports team
26 served on the student council
67 were members of clubs
. . 13 students were members of both a team and a club
. . 9 were on both a team and the student council
. . 11 were a member of both the student council and a club
. . . . 10 students did not participate in any of these activities.
How many graduating students were in all three activities?
With two groups:
. .
With three groups:
. .
Let:. .
There were: students who were in at least one activity.
. . That is: .
So we have:
. . . . . .
Therefore: .
Edit: Too fast for me, Plato!
.
As it is given that ther are 190 students in all 10
Out of which do not participate in any of the events.
i.e. there are only 190 -10 = 180 students who participated in some event
or we can say that the union of all the paricipants of some event is of count 180 students.
Now we Let S=sport team particiapnt
C = student council
Cb = club member
then
190 - 10 = 180 = |S U C U Cb |= |S| + |C| + |Cb| - |S U C| - |SU cb| - |C U Cb| + |S intersection C intersection Cb|
Que is
|S intersection C intersection Cb|=?
|S intersection C intersection Cb|= |S U C U Cb |-|S| - |C| - |Cb| + |S U C| + |SU cb| + |C U Cb|
or |S intersection C intersection Cb|=180 - 111 - 26 - 67 + 13 + 11 + 9 = 9
ans = 9