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Giải mục 3 trang 64, 65 SGK Toán 10 tập 2 - Kết nối tri thức

Từ các chữ số 0, 1, 2, 3 có thể lập được bao nhiêu số thỏa mãn: Khối lớp 10 của một trường trung học phổ thông có ba lớp 10A, 10B, 10C.

Tổng hợp đề thi h♚ọc kì 2 lớp 10 tꦗất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Luyện tập 3

Từ các chữ số 0, 1, 2, 3 có thể lập được bao nhiêu số thỏa mãn: a) Là số tự nhiên có ba chữ số khác nhau? b) Là số tự nhiên chẵn có ba chữ số khác nhau?

Lời giải chi tiết:

a) Từ 4 chữ số 0, 1, 2, 3: - Hàng trăm có 3 cách chọn. - Hàng chục có 3 cách chọn. - Hàng đơn vị có 2 cách chọn. Vậy có tất cả 3.3.2=18 số tự nhiên khác nhau có 3 chữ số được lập từ 0, 1, 2, 3. b) - Trường hợp 1: hàng đơn vị là số 0 như vậy hàng trăm có 3 cách chọn, hàng chục có 2 cách chọn. Có tất cả 1. 2. 3= 6 số có thể lập được. - Trường hợp 2: hàng đơn vị là số 2 như vậy hàng trăm có 2 cách chọn, hàng chục có 2 cách chọn. Có tất cả 1. 2. 2= 4 số có thể lập được. Vậy có thể lập 6+4= 10 số tự nhiên chẵn có ba chữ số khác nhau.

Vận dụng

Khối lớp 10 của một trường trung học phổ thông có ba lớp 10A, 10B, 10C. Lớp 10A có 30 bạn, lớp 10B có 35 bạn, lớp 10C có 32 bạn. Nhà trường muốn chọn 4 bạn để thành lập đội cờ đỏ của khối sao cho có đủ đại diện của các lớp. Hỏi có bao nhiêu cách lựa chọn?

Phương pháp giải:

 Chia 3 trường hợp: -  2 bạn lớp 10A, 1 bạn lớp 10B, 1 bạn lớp 10C. -  1 bạn lớp 10A, 2 bạn lớp 10B, 1 bạn lớp 10C. -  1 bạn lớp 10A, 1 bạn lớp 10B, 2 bạn lớp 10C. Áp  dụng quy tắc nhân tính từng trường hợp có bao nhiêu cách chọn và quy tắc cộng để cộng 3 trường hợp với nhau.

Lời giải chi tiết:

TH1: 2 bạn lớp 10A, 1 bạn lớp 10B, 1 bạn lớp 10C có số cách chọn là: \(C_{30}^2\). 35. 32= 487200( cách) TH2: 1 bạn lớp 10A, 2 bạn lớp 10B, 1 bạn lớp 10C có số cách chọn là: 30.\(C_{35}^2\). 32= 571200 (cách) TH3: 1 bạn lớp 10A, 1 bạn lớp 10B, 2 bạn lớp 10C có số cách chọn là: 30. 35.\(C_{32}^2\)= 520800 (cách) Vậy số cách lựa chọn là: 487200+ 571200 + 520800= 1579200 cách

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