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?

Guest Jun 15, 2021

#2**+2 **

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.

amygdaleon305 Jun 16, 2021