We have the set A of 100 students and three its subsets S (string; 70 elements), W (wooding; 49 elements), and B (brasses; 49 elements).

Let us denote SW the intersection of S and W for brevity; denote SB the intersection of S and B; and denote
WB the intersection of W and B.

Also let us denote SWB the intersection of all the three subsets S, W and B.


We know that the subset S consists of 70 elements, the subset W consists of 49 elements and the subset B consists of 49 elements.

We are also given that SW consists of 20 elements, SB consists of 25 elements, and WB consists of 35 elements.

The question is: how many elements are in SWB?


For any given subset X, let us use the symbol |X| for the number of elements in X.


Then there is a remarkable equality, which connects the number of elements in the set A; in its subsets S, W and B;
in their intersections SW, SB and WB; and in the subset SWB:

|A| = |S| + |W| + |B| - |SW| - |SB| - |WB| + |SWB|.     (1)

under the condition that the union of subsets S, W and B covers the entire A:  A = S U W U B.


Now look how this equality will help us to solve our problem.
Simply substitute the known values into this equality. You will get

100 = 70 + 49 + 49 - 20 - 25 - 35 + |SWB|.                 (2)

|SWB| is the only unknown in this equation, and you can easily find it by isolating.

|SWB| = 100 - (70+49+49) + (20+25+35) = 12.


Answer.  12 students play all 3 instruments.