Từ các chữ số \(1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9\) có thể lập được bao nhiêu số tự nhiên mà mỗi số có 6 chữ số khác nhau và tổng các chữ số hàng chục, hàng trăm, hàng nghìn bằng 8?
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Gọi số cần tìm có dạng: \(\overline{a_{1} a_{2} a_{3} a_{4} a_{5} a_{6}}\) với \(a_{3}+a_{4}+a_{5}=8\)
Ta có: \(8=1+2+5=1+3+4(*)\).
Vậy có 2 cách chọn nhóm 3 số để các số hàng chục, hàng trăm, hàng nghìn có tổng bằng 8.
Bước 1: Chọn ra 3 trong 8 số thỏa mãn \(a_{3}+a_{4}+a_{5}=8\). Theo phân tích (*) có : 2 cách.
Bước 2: Với mỗi bộ ba số chọn ở bước 1 có: \(3!=6\) cách lập số \(\overline{a_{3} a_{4} a_{5}}\).
Bước 3: Chọn ra số \(\overline{a_{1} a_{2} a_{6}}\) theo thứ tự trên. Số cách chọn: \(A_{6}^{3}=120\).
Theo quy tắc nhân số cách chọn theo yêu cầu là: \(2 \cdot 6 \cdot 120\) =1440 số.
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