1 . 设
为大于2的自然数,将二项式
两边同时求导,可以得到一些特别的组合恒等式
,结合课本中杨辉三角研究方法,可以得到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f15fc276a46463377bcecb7c6e174b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb174c123cb7dd2d47237adc5b17acae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5ee37c0c6e04fe8d2647b7563243e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f15fc276a46463377bcecb7c6e174b.png)
您最近一年使用:0次
2 . 已知
表示数
,其中数列
单调递增,且
为正整数.当
时,记所有满足条件的
的个数为
当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec28b5d6e3263275d38599aed15ccd2.png)
______ ;当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b79bd8fd7c11f7ee3f42c409a632b4e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27effd133986a687e5928c1eb1d27b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3a8c295c6019e7b2517a0f6320f4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891c0cae5388125948b70ea4ebc4d9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cdbb0647b2b452f47a95dcf736bae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec28b5d6e3263275d38599aed15ccd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8e6b35ef78852d6a39d8eca26847e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b79bd8fd7c11f7ee3f42c409a632b4e.png)
您最近一年使用:0次
名校
解题方法
3 . 春暖花开季节,小王、小李、小张、小刘四人计划“五・一”去踏青,现有三个出游的景点:南湖、净月、莲花山,假设每人随机选择一处景点,在至少有两人去南湖的条件下有人去净月的概率为__________ .
您最近一年使用:0次
2024-05-09更新
|
1321次组卷
|
3卷引用:吉林省长春市东北师范大学附属中学2024届高三下学期第五次模拟考试数学试题
名校
解题方法
4 . 从集合
的子集中选出
个不同的子集
,且
,则选法有_________ 种.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad8810256459629f91882918fd45597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
您最近一年使用:0次
5 . 若
是一个集合,
是一个以
的某些子集为元素的集合,且满足:①
属于
,空集
属于
;②
中任意多个元素的并集属于
;③
中任意多个元素的交集属于
,则称
是集合
上的一个拓扑.已知函数
,其中[x]表示不大于
的最大整数,当
时,函数
值域为集合
,则集合
上的含有4个元素的拓扑
的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89d1c17a43495542eaade6426cf4c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668efc94065bc0b990673bf77c40eeeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2024-04-29更新
|
188次组卷
|
2卷引用:江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题
6 . 袋中有
个红球,
个黄球,
个绿球.现从中任取两个球,记取出的红球数为
,若取出的两个球都是红球的概率为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d419c30ff40e9b368a3f151f639dac8f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d419c30ff40e9b368a3f151f639dac8f.png)
您最近一年使用:0次
7 . 从2名男生,4名女生中任选3人参加活动,则男生、女生都有人被选中的选法共有______ 种.(用数字作答)
您最近一年使用:0次
2023-10-17更新
|
393次组卷
|
3卷引用:云南省部分名校2024届高三上学期10月联考数学试题
云南省部分名校2024届高三上学期10月联考数学试题(已下线)3.1.3 组合和组合数(第1课时 组合和组合数的性质)(分层练习)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第二册)吉林省延边市第二中学2023-2024学年高二上学期期中考试数学试卷
23-24高三上·上海浦东新·阶段练习
名校
8 . 在某道选词填空题中,共有4个空格、5个备选单词,其中每个空格只有备选单词中的一个正确答案(备选单词中有一个是多余的),则4个空格全部选错的概率是________ .
您最近一年使用:0次
9 . 产品抽样检查中经常遇到一类实际问题,假定在N件产品中有M件不合格品,在产品中随机抽
件做检查,发现
件不合格品的概率为
,其中
是
与
中的较小者,
在
不大于合格品数(即
)时取0,否则
取
与合格品数之差,即
.根据以上定义及分布列性质,请计算当N=16,M=8时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6024f4805db0363088fb74b8c4c8383.png)
_____ ;若
,
,请计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665924c7db172f1e1c26bdf998a540df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b130933397267e76c4d2c720260d6a.png)
_____ .(用组合数表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07ed4354c10be176c28883165b6b3e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aec95ea06af2f1bac2b245163a3c6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adb213b62fdf991674caace7a218365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6024f4805db0363088fb74b8c4c8383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2dbbaba1b658fe7476197104a2b1a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd40c3e2e1a5bf8493af1047fa8602ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665924c7db172f1e1c26bdf998a540df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b130933397267e76c4d2c720260d6a.png)
您最近一年使用:0次
名校
10 . 已知袋中有
(
为正整数)个大小相同的编号球,其中黄球8个,红球
个,从中任取两个球,取出的两球是一黄一红的概率为
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65beded5829ca2846ccd3cade755ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
您最近一年使用:0次
2023-03-15更新
|
748次组卷
|
7卷引用:上海市建平中学2023届高三上学期11月月考数学试题
上海市建平中学2023届高三上学期11月月考数学试题上海市曹杨第二中学2023届高三下学期2月月考数学试题上海市南模中学2023届高三下学期5月月考数学试题(已下线)第05讲 古典概型与概率的基本性质(八大题型)(讲义)-2上海市七宝中学2019-2020学年高二下学期4月月考数学试题(已下线)核心考点10计数原理(2)上海市曹杨第二中学2023-2024学年高二下学期期末考试数学试卷