In a group of 36 girls, each one can either stitch or weave or can do both. If 25 girls can stitch and 17 can stitch only, how many can weave only?

Given:

Total number of girls: n(S ∪ W) = 36

Girls who can stitch: n(S) = 25

Girls who can stitch only: n(S - W) = 17

Girls who can weave only: n(W - S) = ?

First find how many can do both, we use the formula:

n(S - W) = n(S) - n(S ∩ W)

Substituting the values in above, we get:

17 = 25 - n(S ∩ W)

⇒ n(S ∩ W) = 25 - 17

⇒ n(S ∩ W) = 8

So, 8 girls can do both.

Since every girl in the group of 36 does at least one activity, the total is the sum of "stitch only," "weave only," and "both."

n(S ∪ W) = n(S - W) + n(W - S) + n(S ∩ W)

n(W - S) = n(S ∪ W) - n(S - W) - n(S ∩ W) $\quad$[Solving for n(W - S)]

Substituting the values in above, we get:

n(W - S) = 36 - 17 - 8

n(W - S) = 36 - 25

n(W - S) = 11

∴ 11 girls can weave only.

The Venn diagram is shown below: