In a recent survey of 100 women, the following information was gathered.
42 use shampoo A.
38 use shampoo B.
34 use shampoo C.
7 use shampoos A and B.
9 use shampoos A and C.
11 use shampoos B and C.
5 use all three.
How many are using shampoos A and C, but not B?
_____women
9 use shampoos A and C. This set of 9 also includes people who would use B.
5 people use all three
9 - 5 = 4
To find the number of women using shampoos A and C, but not B, you can use the principle of inclusion-exclusion.
First, we sum up the number of women using shampoos A and C:
Number of women using shampoos A and C = Number using shampoos A + Number using shampoos C - Number using all three
Number using shampoos A and C = 42 + 34 - 5 = 71
Next, we need to subtract the number of women using shampoos A, C, and B, because we only want those using shampoos A and C, but not B:
Number of women using shampoos A and C, but not B = Number using shampoos A and C - Number using shampoos A, C, and B
Number using shampoos A and C, but not B = 71 - 9 = 62
Therefore, there are 62 women using shampoos A and C, but not B.