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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?

 Jun 15, 2021
 #1
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By Inclusion-Exclusion, there are 6 student who do all three activities.

 Jun 15, 2021
 #2
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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. 

 Jun 16, 2021

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