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# Sets A,B and C have some elements in common.If 16 elements

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[#permalink]  30 Jun 2006, 07:56
amansingla4 wrote:
HongHu wrote:
See if this helps (from the basic priniciple sticky):

HongHu wrote:
Formula:

Total = N(A) + N(B) + N(C) - N(A n B) - N(A n C) - N(C n B) + N(A n B n C)

If instead of numbers for (A n B) and (A n C) and (C n B), what is given is the total number of people who choose exactly two items, then the formula becomes:

Total = N(A) + N(B) + N(C) - (N(choose exactly two items)) - 2N(choose all three items)

Also,
Total = N(A) + N(B) + N(C) - (N(choose at least two items)) - N(choose all three items)

Can you please explain these two formulas?

Regards,
Aman

Hmmm let me see. Say, total is 100 people, 60 bought Apples, 50 bought Bananas, 35 bought Cranberries. If we know that number of people who bought all three is 10, then we know 25 people bought exactly two of the three, and that 35 people bought more than one fruit (or at least two fruits).

However, in this case we do not know how many people bought A&B, A&C and B&C exactly. It might be the case that 15 people bought A&B, 20 people bought B&C and 20 people bought A&C. The point that needs to be noticed is that when we say 20 people bought B&C they may have or have not bought A as well. In our case 10 of the 20 actually bought all three. I know this sometimes can be very confusing. You just need to make sure if you are talking about "exactly two" or "at least two". Making a Venn gram will help most of the time.
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[#permalink] 30 Jun 2006, 07:56
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# Sets A,B and C have some elements in common.If 16 elements

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