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#### bergausstein

##### Active member

- Jul 30, 2013

- 191

1. Say the football team F, the basketball team B, and the track team T, decide to form a varsity club V. how many members will V have if $n\left(F\right)\,=\,25,\,n\left(B\right)\,=\,12,\,n\left(T\right)\,=\,30$ and no person belongs to two teams?

Solution. $n\left(F\right)+n\left(B\right)+n\left(T\right)\,=\,67$ there's no possibility of overlap.

a. If in problem 1, $n\left(F\cap T\right)\,=\,6$ but there are no members of B who are in F or T then what is $n\left(V\right)$?

Solution. since there are six persons who belong to T and F i will subtract 6 from 67 which is 61.

b. If in problem 1.a $n\left(F\cap T\right)\,=\,6$, $n\left(T\cap B\right)\,=\,4$ and $n\left(F\cap B\right)\,=\,0$ then what is $n\left(V\right)$?

Solution. there are now 10 persons that belong to two teams i will subtract these number from 67 and I will have 57.

c. if in problem 1.b $n\left(F\cap T\right)\,=\,6$, $n\left(T\cap B\right)\,=\,4$ and $n\left(F\cap B\right)\,=\,3$, and there are 2 three letter men that is $n\left(F\cap B\cap T\right)\,=\,2$, then what is $n\left(V\right)$?

in part C i don't understand the part where it say "there are 2 three letter men".

but this is what i Tried. there are now 13 persons who belong to two teams and 2 persons who are member of the three teams. 67-15 = 54-2 = 52.

please check if my answers were correct.