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In a music class, 12 students can play flute, 11 can play guitar and 10 can play violin. 6 students can play flute as well as guitar and 3 out of these can also play violin. 3 students can play only guitar and 4 students can play only violin. How many students can play only flute?

In a music class, 12 students can play flute, 11 can play guitar and 10 can play violin. 6 students can play flute as well as guitar and 3 out of these can also play violin. 3 students can play only guitar and 4 students can play only violin. How many students can play only flute? Correct Answer 5

According to the given information,

12 students can play flute, 11 can play guitar and 10 can play violin

6 students can play flute as well as guitar and 3 out of these can also play violin i.e., 3 students can play all the three

3 students can play only guitar and 4 students can play only violin

Number of students who can play guitar as well as violin = 11 – (3 + 3 + 2) = 3

Number of students who can play violin as well as flute = 10 – (4 + 3 + 2) = 1

Drawing the Venn diagram,

[ alt="F1 R.R 5.6.20 Pallavi D7" src="//storage.googleapis.com/tb-img/production/20/06/F1_R.R_5.6.20_Pallavi_D7.png" style="width: 187px; height: 131px;">

Number of students who can only play flute = 12 – (3 + 3 + 1)

= 12 – 7

= 5

Hence, “5” is the correct answer.

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