whats the formula for "atleast 2" in sets?

so in the solution at AB it is given that atleast two= exactly two + all three = 60+12=72

but isnt the formula for atleast 2= A[∩B+ B∩C+ C∩A - 2(A∩B∩C)? (got to know from MBA Wallah)]

so the answer, which i am getting, is = 30+20+10-2.12=60-24=36

can anyone answer this? i am so confused

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Comments (3)

A
aarushmfc
11mos

There's no need to apply a formula here tbh it's a 10 second answer

They asked minimum 2 courses so that's people who are enrolled in exactly 2 courses which is given 60 in the question and people who are in all 3 which is also given 12 so it's automatically 60+12 that's 72

2
A
aarushmfc
11mos
Correct

The reason the formula won't work is (if I'm not wrong) the reason u subtract 2 times A interection B intersection C is because you've triple counted it in the first 3 terms since A intersection B includes the students who have all 3. But in the question you're given only the people who are in exactly 2 courses so that's not A intersection B that's A intersection B minus the people enrolled in all 3 courses which is 12

Similarly for the other 2 terms

1
I
ipmgetsmogged
OP11mos

oh got it, tysm

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