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Câu 57 trang 93 SGK Đại số và Giải tích 11 Nâng cao

Xét hồ sơ mạng điện có 9 công tắc, trong đó mỗi công tắc có hai trạng thái đóng và mở.
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Xét hồ sơ mạng điện có 9 công tắc, trong đó mỗi công tắc có hai trạng thái đóng và mở.

LG a

Hỏi mạng điện có thể có bao nhiêu cách đóng – mở 9 công tắc trên ?

Lời giải chi tiết:

Mỗi công tắc có hai trạng thái đóng và mở. Mạng điện có 9 công tắc.

Theo qui tắc nhân, mạng điện có 29 = 512 cách đóng – mở 9 công tắc trên.

LG b

Hỏi mạng điện có bao nhiêu cách đóng – mở 9 công tắc trên để thông mạch từ A đến B (tức là có dòng điện đi từ A đến B) ?

Lời giải chi tiết:

 

Mạng điện thông mạch từ A đến B khi và chỉ khi cả ba khối M, N và P đều thông mạch. +) Khối M có \(2^4= 16\) cách đóng – mở 4 công tắc trong đó chỉ có 1 cách không thông mạch (đó là mở cả 4 công tắc). Do đó có 15 cách đóng – mở 4 công tắc để thông mạch của khối M. +) Khối N có \(2^2=4\) cách đóng  - mở công tắc, trong đó chỉ có 1 cách không thông mạch (đó là mở cả 2 công tắc). Do đó có 3 cách đóng – mở 2 công tắc để thông mạch của khối N. +) Khối P có \(2^3=8\) cách đóng  - mở công tắc, trong đó chỉ có 1 cách không thông mạch (đó là mở cả 3 công tắc). Do đó có 7 cách đóng – mở 3 công tắc để thông mạch của khối P. Theo qui tắc nhân, mạng điện có \(15.3.7 = 315\) cách đóng – mở 9 công tắc để thông mạch.

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