Có 8 bạn học sinh lớp 11a trong đó có An và Bình được xếp ngẫu nhiên theo một hàng ngang

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Có 12 học sinh gồm 3 học sinh lớp A; 3 học sinh lớp B và 6 học sinh lớp C trong đó có hai bạn An và Bình cùng thuộc lớp C. Xếp ngẫu nhiên 12 học sinh này thành một hàng ngang, xác suất để mỗi học sinh lớp B luôn xếp giữa hai học sinh lớp C đồng thời hai bạn An và Bình luôn xếp cạnh nhau bằng

A.  1 13860

B.  1 210

C.  1 4620

D.  1 3080

Xếp ngẫu nhiên 10 học sinh gồm 2 học sinh lớp A, 3 học sinh lớp B và 5 học sinh lớp C thành một hàng ngang. Tính xác suất để không có hai học sinh cùng lớp đứng cạnh nhau.

Có 12 bạn học sinh trong đó có đúng một bạn tên A và đúng một bạn tên B. Xếp ngẫu nhiên 12 học sinh vào một bàn tròn và một bàn dài mỗi bàn 6 học sinh. Xác suất để hai bạn A và B ngồi cùng bàn và cạnh nhau bằng

A.  1 5

B.  1 6

C.  1 10

D.  1 12

Xếp ngẫu nhiên tám học sinh gồm bốn học sinh nam [trong đó có Hoàng và Nam] cùng bốn học sinh nữ [trong đó có Lan] thành một hàng ngang. Xác suất để trong tám học sinh trên không có hai học sinh cùng giới đứng cạnh nhau, đồng thời Lan đứng cạnh Hoàng và Nam là

A .   1 560

B .   1 1120

C .   1 35

D .   1 280

Xếp ngẫu nhiên 10 học sinh gồm 5 học sinh nam và 5 học sinh nữ thành một hàng ngang. Xác suất để trong 10 học sinh trên không có hai học sinh cùng giới tính đứng cạnh nhau, đồng thời Hoàng và Lan không đứng cạnh nhau bằng

A.   1 450 .

B.   8 1575 .

C.   1 175 .

D.   4 1575 .

Xếp ngẫu nhiên 10 học sinh gồm 5 học sinh nam và 5 học sinh nữ thành một hàng ngang. Xác suất để trong 10 học sinh trên không có hai học sinh cùng giới tính đứng cạnh nhau, đồng thời Hoàng và Lan không đứng cạnh nhau bằng

A.  1/450

B.  8/1575

C.  1/175

D.  4/1575

Xếp ngẫu nhiên 10 học sinh gồm 2 học sinh lớp 12A, 3 học sinh lớp 12 B và 5 học sinh lớp 12C thành một hàng ngang. Xác suất để trong 10 học sinh trên không có 2 học sinh cùng lớp đứng cạnh nhau bằng

A.

B. 

C.

D.  

Xếp ngẫu nhiên tám học sinh gồm bốn học sinh nam [trong đó có Hoàng và Nam] cùng bốn học sinh nữ [trong đó có Lan] thành một hàng ngang. Xác suất để trong tám học sinh trên không có hai học sinh cùng giới đúng cạnh nhau, đồng thời Lan đứng cạnh Hoàng và Nam là

A. 1 560

B. 1 1120

C. 1 35

D. 1 280

có 8 bạn học sinh lớp 11a trong đó có an và bình được xếp ngẫu nhiên theo một hàng ngang. Tính xác suất P để an và bình ngồi cạnh nhau

Có 8 học sinh trong đó có 2 bạn tên A và B. Xếp ngẫu nhiên 8 học sinh trên theo một hàng ngang. Xác xuất để hai bạn A và B đứng cạnh nhau là

Đáp án C

Xếp ngẫu nhiên  học sinh thành một hàng có 10! ⇒n[Ω] =10!

Gọi biến cố A : “Xếp  học sinh thành một hàng sao cho An và Bình đứng cạnh nhau”.

Xem An và Bình là nhóm X .

Xếp X và học sinh còn lại có 9! cách.

Hoán vị An và Bình trong X có 2! cách.

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Có 8 bạn học sinh lớp 11A trong đó có An và Bình được xếp ngẫu nhiên theo một hàng ngang. Tính xác suất để An và Bình ngồi cạnh nhau.

A.

$\frac{1}{8}.$

B.

$\frac{1}{25}.$

C.

$\frac{1}{4}.$

D.

$\frac{1}{64}.$

Đáp án và lời giải

Đáp án:C

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