Stolyar's approach is the most concise and clear. However, if on the official test this question appears last in the maths section and you happened to have 15 minutes left
, check yourself as follows:
At least one means one or more (i.e. in our case favourable conditions are: one woman in a pair, two women in a pair). Thus,
P (one woman in a pair (and one man)) = C(10,1)*C(10,1)=100.
We use multiplication because both outcomes are parts of one set.
P (two women) = C(10,2)=45.
Add the outcomes - 100+45=145