Math man 120, Chinese man 80, and both men 75, that is, apart from these 75 men, there are only 45 math men and only 5 Chinese men.

Therefore, the total number of boys =75+45+5= 125.

The total number is 260, so the total number of girls =260- 125= 135.

135, there are 80 women in mathematics and 20 women in Chinese, so the number of girls who take part in both events = 120+80-135 = 65.

Therefore, female only mathematics = female mathematics-female biathlon =80-65= 15.