Question 1183899
you are stating that.....


there are a total of 35 students.


18 sang
19 danced
7 sand and danced.


your numbers don't add up.


first of all.


if there are 35 students total,  and 18 of them sang and 19 of them danced, that gets you a total of 37 students, assuming that none of hem both sang and danced.


in order for there to be 35 students total, 2 of them must have sang and danced.


that would give you 16 who sang only and 17 who danced only and 2 who sang and danced for a total of 35 students.


if you had 18 students who sang and 19 students who danced and 7 who sang and danced, and the 7 who sang and danced were included in the number of those who sang and those who danced, then you would get:


11 sand only and 12 danced only and 7 sang and danced.


that would give you a total of 30 students.


if you had 18 students who sang and 19 students who danced and 7 who sand and danced, and the 7 who sand and danced were not included in the number of those who sang and those who danced, then you would get:


18 sand only and 19 danced only and 7 sang and danced.


that would give you a total of 44 students.


bottom line:


you have a prblem with your numbers.


it could not be 35 students.
it would only be 30 or 44.


here are my two venn diagrams that capture what i think is the case.


the first venn diagram is assuming that the 7 who sang and danced were included in the number of those who sang and those who danced.


the second venn diagram is assuming that the 7 who sang and danced were not included in the number of those who sang and those who danced.


<img src = "http://theo.x10hosting.com/2021/082602.jpg" >


neither of these two options will get you a total of 35 students.


you need to go back and check again what they are asking you to do.