Posted by **Anonymous** on Monday, February 6, 2012 at 2:35pm.

In a recent survey of 100 women, the following information was gathered.

30 use shampoo A.

43 use shampoo B.

33 use shampoo C.

13 use shampoos A and B.

7 use shampoos A and C.

5 use shampoos B and C.

3 use all three.

How many are using shampoo A only (Region I)?

- math -
**Reiny**, Monday, February 6, 2012 at 2:56pm
make a Venn diagram of 3 intersecting circles called A, B , and C

Put 3 in the intersection of all 3

Now look at the intersection of A and B, which is given as 13

But 3 have already been entered, so put 10 in the remaining part of A intersect B

in the same way the remaining part of A intersect C would be 4 and

the remaining part of B intersect C would be 2

now look at circle A, we have already entered 17, but there are 30 using A

So 13 would be using only A

Only B would be 28 and only C would be 24

Adding all those up only gives us 84

So unless I made some silly arithmetic error, it looks like 16 of the women don't use any of the three shampoos.

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