Final answer:
Using the principle of inclusion-exclusion, there are 28 individuals who can dance salsa, tango, or both, as calculated by adding the number of individuals who can dance salsa and tango and then subtracting the number of individuals who can dance both.
Step-by-step explanation:
To determine the number of individuals who can dance salsa, tango, or both, we can use the principle of inclusion-exclusion. According to the given information:
- 26 can dance salsa (S)
- 11 can dance tango (T)
- 9 can dance both salsa and tango (S ∩ T)
- 36 can dance salsa and tango combined (S ∪ T)
The formula to find the total number of individuals who can dance either salsa or tango or both is:
Total = S + T - (S ∩ T)
If we replace the values from the given information, we get:
Total = 26 (S) + 11 (T) - 9 (S ∩ T)
Total = 26 + 11 - 9
Total = 37 - 9
Total = 28
So, according to the inclusion-exclusion principle, there are 28 individuals who can dance salsa, tango, or both.
Note: The given number of 36 individuals for 'salsa and tango combined' is incorrect based on the principle of inclusion-exclusion since 26+11-9 = 28, not 36. There might be some mistake in the provided information or there might be additional factors not considered in our simple calculation.