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Answer :
17 are older than 16 years old and 12 are taller than 170 cm
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Final answer:
By using the principle of inclusion-exclusion, we calculate that all 20 girls on the basketball team are either over 16 years old or taller than 170 cm, as the sum of the individual criteria minus the intersection equals the total number of girls on the team.
Explanation:
To determine how many of the girls on the basketball team are either over 16 years old or taller than 170 cm, we can use the principle of inclusion-exclusion. According to the information provided, there are 20 girls on the team in total, of which 17 are over 16 years old, 12 are taller than 170 cm, and 9 satisfy both criteria. The principle of inclusion-exclusion states that the number of elements in the union of two sets is equal to the sum of the sizes of each set minus the size of their intersection.
Using this principle:
Number of girls over 16 years old: 17
Number of girls taller than 170 cm: 12
Number of girls who are both over 16 and taller than 170 cm: 9
The calculation would be as follows:
17 (over 16) + 12 (taller than 170 cm) - 9 (both) = 20
Therefore, there are 20 girls on the team who are either older than 16 or taller than 170 cm.
