Có bao nhiêu cách xếp 4 bạn nam và 2 bạn nữ thành một hàng dọc

Có bao nhiêu số có \(3\) chữ số được lập thành từ các chữ số \(3,2,1\)?

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nếu câu trả lời hữu ích nhé!

• thanhduc25052011

• 06/05/2020

• Cám ơn
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XEM GIẢI BÀI TẬP SGK TOÁN 11 - TẠI ĐÂY

Xếp chỗ cho 4 bạn nam có 4!=24 cách

Xếp 2 bạn nữ vào 2 vị trí đầu và cuối dãy 4 bạn na có 2!=2 cách

Vậy số  cách sắp xếp 6 bạn thành hàng dọc sao cho bốn bạn nam cạnh nhau là 2.24=48(cách)

Hay nhất

Chọn D

Vì 6 nữ đứng cạnh nhau nên xem 6 nữ thành 1 nhóm, và 4 bạn nam có 5! cách.

6 bạn nữ có thể hoán vị cho nhau, có 6! cách.

Vậy số cách xếp: 5!.6!=86400.

Có bao nhiêu cách xếp chỗ cho 4 bạn nữ và 6 bạn nam ngồi vào 10 ghế mà không có hai bạn nữ nào ngồi cạnh nhau, nếu. Bài 2.14 trang 67 Sách bài tập (SBT) Đại số và giải tích 11 – Bài 2. Hoán vị – Chỉnh hợp – Tổ hợp

Có bao nhiêu cách xếp chỗ cho 4 bạn nữ và 6 bạn nam ngồi vào 10 ghế mà không có hai bạn nữ nào ngồi cạnh nhau, nếu

a)      Ghế sắp thành hàng ngang ?

b)      Ghế sắp quanh một bàn tròn ?

a)      Xếp 6 nam vào 6 ghế cạnh nhau. Có 6! cách.

Giữa các bạn nam có 5 khoảng trống cùng hai đầu dãy, nên có 7 chỗ có thể đặt ghế cho nữ.

Bây giờ chọn 4 trong 7 vị trí để đặt ghế. Có \(C_7^4\) cách.

Quảng cáo

Xếp nữ vào 4 ghế đó. Có 4! cách.

Vậy có \(6!.C_7^4.4! = 120.7!\) cách xếp mà không có hai bạn nữ nào ngồi cạnh nhau.

b)      Xếp 6 ghế quanh bàn tròn rồi xếp nam vào ngồi. Có 5! cách.

Giữa hai nam có khoảng trống. Xếp 4 nữ vào 4 trong 6 khoảng trống đó. Có \(A_6^4\) cách.

Theo quy tắc nhân, có \(5!.A_6^4 = 43200\) cách. 

Có 4 bạn nam và 2 bạn nữ. Hỏi có bao nhiêu cách sắp xếp các bạn trên vào một ghế dài có 8 chỗ sao cho các bạn nam ngồi cạnh nhau thành một nhóm, các bạn nữ ngồi cạnh nhau thành một nhóm và hai nhóm này cách nhau đúng một chỗ ngồi?

A.

A. 144

B.

B. 192

C.

C. 152

D.

D. 164

Đáp án và lời giải

Đáp án:B

Lời giải:

Chọn đáp án B

Nam

và nữ . +) Xếp có 4.4! cách (1, 2, 7, 8) +) Xếp có 1.2! cách. Tóm lại có tất cả 4.4!.1.2 = 192 cách.

Đáp án đúng là B

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