题目
What is the probability P that A and B are both selected when you select 40 people out of a group of 100 (A and B included)?
选项
C.The two quantities are equal.
D.The relationship cannot be determined from the information given.
解析
我们已经选定A和B两人,因此需要从剩余的$100-2=98$人中再选出38人。
选法数为$\binom{98}{38}$
总选法数为$\binom{100}{40}$
概率:
p = \frac{\binom{98}{38}}{\binom{100}{40}}
p = \frac{98!}{38! \cdot 60!} \times \frac{40! \cdot 60!}{100!}
p = \frac{98! \cdot 40!}{38! \cdot 100!} = \frac{40 \times 39}{100 \times 99} = \frac{26}{165}
因此,答案为选项C