We don't know the intersection of all three circles, so label it x

Now go to the intersection of two of the circles, say, the M and B circles

It says that sum is 15, but we have already counted x of them, so in the remaining part of the football-shaped region is 15-x

Do that for the other two intersection of pairs to have 10-x and 7-x

Now go to the whole circles, start with M

We have already counted, 15-x, x, and 7-x

or 22-x

But the whole math circle contains 32, so the open part must be 32-(22-x) = 10+x

Do the same with the other whole circles and get

20+x and 3+x

Now add them all up.

We can use a short-cut here, we know that everything in the Math circle is 32, so ..

32 + 10-x + 20+x + 3+x = 70

x = 5

ii) 5 take all three subjects

ii) add up all the parts in the outer parts of the circle which do not intersect with any other circles

that is,

Math only = 27

Biology only = 25

Physics only = 8

or

using the formula:

N(M or P or B) = N(M) + N(B) + N(P) - N(M and P) - N(M and B) - N(P and B) + N(M and P and B)

70 = 32+45+20 - 7 - 15 -10 + x

x= 5