问题 填空题

将24个志愿者名额分配给3个学校,则每校至少有一个名额且各校名额互不相同的分配方法共有   种.

答案

  222

用4条棍子间的空隙代表3个学校,而用表示名额.如

      

表示第一、二、三个学校分别有4,18,2个名额.

若把每个“”与每个“”都视为一个位置,由于左右两端必须是“|”,故不同的分配方法相当于个位置(两端不在内)被2个“|”占领的一种“占位法”.

“每校至少有一个名额的分法”相当于在24个“”之间的23个空隙中选出2个空隙插入“|”,故有种.

又在“每校至少有一个名额的分法”中“至少有两个学校的名额数相同”的分配方法有31种.

综上知,满足条件的分配方法共有253-31=222种.

[解法二] 设分配给3个学校的名额数分别为,则每校至少有一个名额的分法数为不定方程

    

的正整数解的个数,即方程的非负整数解的个数,它等于3个不同元素中取21个元素的可重组合:

又在“每校至少有一个名额的分法”中“至少有两个学校的名额数相同”的分配方法有31种.

综上知,满足条件的分配方法共有253-31=222种.  

阅读理解

"Get out of the plane!" Justin shouted. Teddy and he dropped to the ground…

When Kathy and Victor reached the edge of the meadow, flames of the fire were shooting more than five meters into the air.

Kathy couldn't believe what she was seeing.One glance told her they needed medical attention immediately.She questioned Victor, "Are you able to find someone nearby for help?"

"There are no farmers, nor villagers nearby," he replied.

"I'm a distance runner, and I'll go for help." Looking at the seriously injured men, Kathy said to Victor, "It may take me several hours to get out." She started out.

When she was 23, Kathy set a women's record in a Marathon of 42 kilometers.But now she was running the race of life. She had nearly 30 kilometers of hard wilderness to cover to get help.

Kathy had been running for two hours.This was far back into the wilderness.The country path was growing vague.She stopped to take a quick compass reading.Yes, she had run almost for more than 20 kilometers.Her heart fell, her muscle aching.And finally she saw her car in the distance.

She jumped into the car and sped away.She reached a holiday house and called the police.

During the wait, she walked around, relaxing her legs and drinking water. It took almost two hours for a police helicopter to reach her at the trail end.They needed her for one more task.

小题1:Who actually had the airplane accident?

A.Justin and Teddy

B.Kathy and Victor

C.Justin himself

D.Kathy herself小题2:The underlined part "Now, she was running the race of life" means that ____.

A.Kathy would set up a new record

B.Kathy would run a race alone

C.Kathy was running for the lives of others

D.Kathy couldn't rely on Victor this time小题3:Kathy stopped to have a look at her compass because ____.

A.she wasn't sure of her own memory

B.she had completely lost her way

C.the country path was getting vague

D.there was only the wilderness小题4:What do you think Kathy's final task would be?

A.Giving the injured food and drinks.

B.Showing the police the crash site.

C.Going back to put out the big fire.

D.Taking the injured to the hospital.

判断题