Concept explainers
A salon offers three services-manicures, massages, and hair styling. Five clients come in for all three services. Forty clients come in for both hair styling and manicures. Thirty-five clients come in for both manicures and massages. Fifteen clients come in for both hair styling and massages. Ten clients come in only for massages. Five clients only come in for hair styling and only two clients come in for just manicures. How many total clients are represented by the data?
To calculate:How many total clients are represented by the data?
Answer to Problem 26P
97.
Explanation of Solution
Given information: 5 clients come for all three services.
40 clients come in for both hair styling and manicures.
35 clients come in for both manicures and massages.
15 clients come in for both styling and massages.
10 clients come in only for massages.
5 clients only come in for hair styling.
2 clients come in for just manicures.
Calculation: Let
using above data we plot the vein diagram
from the above vein diagram, we can say that
Now we can find the region that does not includes
Now we find the region that does not includes
finally ,we find the region that does not includes
we know the principal of inclusion and exclusion
Total number of clients are 97.
Chapter 3 Solutions
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