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Câu 11 trang 63 SGK Đại số và Giải tích 11 Nâng cao

Xét mạng đường nối các tỉnh A, B, C, D, E, F, G, trong đó số viết trên một cạch cho biết số con đường nối hai tỉnh nằm ở hai
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Đề bài

Xét mạng đường nối các tỉnh A, B, C, D, E, F, G, trong đó số viết trên một cạch cho biết số con đường nối hai tỉnh nằm ở haiđầu mút của cạnh (h. 2.2). Hỏi có bao nhiêu cách đi từ tỉnh A đến tỉnh G ?

Phương pháp giải - Xem chi tiết

Liệt kê các trường hợp có thể đi từ A đến G. Dùng quy tắc nhân đếm số cách đi trong từng TH. Dùng quy tắc cộng suy ra số cách đi cần tìm.

Lời giải chi tiết

Có 4 phương án đi qua các tỉnh A đến G là :a. A → B → D → E → Gb. A → B → D → F → Gc. A → C → D → E → Gd. A → C → D → F → GTheo quy tắc nhân, ta có :Phương án a: A → B → D → E → GCó \(2.3.2.5 = 60\) cách đi;Phương án b: A → B → D → F → GCó \(2.3.2.2 = 24\) cách đi;Phương án c: A → C → D → E → GCó \(3.4.2.5 = 120\) cách đi;Phương án d: A → C → D → F → GCó \(3.4.2.2 = 48\) cách đi.Theo quy tắc cộng, ta có : \(60 + 24 + 120 + 48 = 252\) cách đi từ A đến G.

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