Of the 35 students in my class, 11 practice taekwondo, 11 play piano, and 20 take lessons at MS. 4 students play piano and go to MS, 3 students do taekwondo and play piano, 5 students go to MS and practice taekwondo, and 3 students do none of these. How many students do all 3?
+526 Let n(P) play piano, n(T) take taekwondo and n(M) take lessons then
n(U) = 35 [Universal set]
n(T) = 11
n(P) = 11
n(M) = 20
n(P∩M) = 4
n(T∩P) = 3
n(M∩T) = 5
n(P∪T∪M)' = 3
⇒n(P∪T∪M) = 35 - 3 = 32
Now subsittute all these values in the formula
n(P∪T∪M) = n(P) + n(T) + n(M) - n(P∩M) - n(T∩P) - n(M∩T) + n(P∩T∩M)
Then you'll get n(P∩T∩M).
I hope its clear.
