Of 30 students, 20 could play the piano, 5 the flute and 6 the violin. 3 violinists could also play the piano but only one of these 3 could also play the flute. 5 students could play both the piano and the flute. None of these students could play any other type of musical instrument. How many students played the piano and the flute but not the violin?

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ygkdzmgtnj ygkdzmgtnj

23-08-2022
Mathematics

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Of 30 students, 20 could play the piano, 5 the flute and 6 the violin. 3 violinists could also play the piano but only one of these 3 could also play the flute. 5 students could play both the piano and the flute. None of these students could play any other type of musical instrument. How many students played the piano and the flute but not the violin?

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mickymike92 mickymike92 · Answer 1 · 2022-08-25T16:24:35+02:00

The number of students that played the piano and the flute but not the violin is 4 students.

What is the number of students that play the piano and the flute but not the violin?

The number of students that play the piano and the flute but not the violin is determined as follows:

Number of students that play all three instruments = 1

Number of students that could play the Piano and Flute = 5

Number of students that could play the Piano and Flute and not the Violin = 5 - 1

Number of students that could play the Piano and Flute and not the = 4

In conclusion, the number of students that play the Piano and Flute but not the Violin is obtained from subtracting the number of students that could play all three instruments from the Number of students that could play the Piano and Flute.

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