一些需要帮忙的题目。希望大家踊跃回答，请写说明，不要只是答案

麻倉枼

1. 铅笔盒里有30支铅笔，一共5种颜色，每种颜色6支，问A闭上眼睛挑选的话，最少要挑多少次才能保证每种颜色都挑两支。 2. 请看图片； 3. 逻辑题： 8. The painter Peter Brandon never dated his works, and their chronology is only now beginning to take shape in the critical literature. A recent dating of a Brandon self-portrait to 1930 is surely wrong. Brandon was 63 years old in 1930, yet the painting shows a young, dark-haired man-obviously Brandon, but clearly not a man of 63. Which of the following, if justifiably assumed, allows the conclusion to be properly drawn? (A) There is no securely dated self-portrait of Brandon that he painted when he was significantly younger than 63. (B) In refraining from dating his works, Brandon intended to steer critical discussion of them away from considerations of chronology. (C) Until recently, there was very little critical literature on the works of Brandon. (D) Brandon at age 63 would not have portrayed himself in a painting as he had looked when he was a young man. (E) Brandon painted several self-portraits that showed him as a man past the age of 60. 我想知道推断的步骤。。谢谢大家

麻倉枼

第一题我的看法是：

2*【C(1,30）+C（1,24）+C（1,18）+C（1,12）+C(1,6)】 = 180

因为是exactly 2, 所以一开始有30支笔，随机选就是C(1，30)种方法，然后选两支以后，我们不可以再抽同样的颜色，所以总数变成30-6，因为每种颜色有6支笔，然后就是C(1，24) *2，如此类推，
最后总数为180，我觉得这个答案看上去OK吧？还是这个是at most多少次而不是at least 多少次

麻倉枼

更新第一题数学题的原题：


There are 30 pencils(6 sets of 5 different colors). A man is taking out pencils one by one blindfoldedly. How many pencils does he need to pick up so that he is gauranteed to have 2 pencils of each color?
A) 24
B) 12
C) 10
D) 14
E) 26

麻倉枼

数学答案找出来了，

E. 26

worst case:
4*6 +2 = 26

前面4种颜色全部都挑过，剩下最后一种颜色随便两支笔

麻倉枼

请回答，请说明推理方式。。