từ các số {0,1,2,3,4,5,6,7}có thể tạo thnàh bao nhiêu số chẵn có 5 chữ sô a) bất kì b) các chữ số khác nhau c) pải có bắt buộc số 2 và 3 trong 5 số (các chữ số khác nhau)

Đáp án:

Giải thích các bước giải:

a) có 7.8.8.8.8=28672 số

b)có 7.7.6.5.4=5880 số có các chữ số khác nhau

c)có 6.5.4.5!-5.4.4!=13920 số

\[\begin{array}{l} A = \left\{ {0;\,\,1;\,\,2;\,\,3;\,\,4;\,\,5;\,\,6;\,\,7} \right\}\\ a)\,\,\,Goi\,\,\,so\,\,can\,\,tim\,\,co\,\,dang:\,\,\overline {{a_1}{a_2}{a_3}{a_4}{a_5}} .\\ Ta\,\,co:\,\,{a_1} \ne 0 \Rightarrow {a_1}\,\,co\,\,\,7\,\,\,cach\,\,chon.\\ {a_2},\,\,{a_3},\,\,{a_4},\,\,{a_5}\,\,\,deu\,\,co\,\,8\,\,cach\,\,chon.\\ \Rightarrow co\,\,{7.8^4}\,\,\,so\,\,co\,\,5\,\,\,\,\,chu\,\,so.\\ b)\,\,Goi\,\,\,so\,\,can\,\,tim\,\,co\,\,dang:\,\,\overline {{a_1}{a_2}{a_3}{a_4}{a_5}} .\\ Ta\,\,co:\,\,{a_1} \ne 0 \Rightarrow {a_1}\,\,co\,\,\,7\,\,\,cach\,\,chon.\\ {a_2} \ne {a_1} \Rightarrow {a_2}\,\,\,co\,\,7\,\,cach\,\,chon.\\ {a_3}\,\,\,co\,\,6\,\,cach\,\,chon.\\ {a_4}\,\,\,co\,\,5\,\,cach\,\,chon.\\ {a_5}\,\,\,co\,\,4\,\,cach\,\,chon.\\ \Rightarrow co\,\,\,7.7.6.5.4 = 5880\,\,cach\,\,chon.\\ c)\,\,\,Goi\,\,\,so\,\,can\,\,tim\,\,co\,\,dang:\,\,\overline {{a_1}{a_2}{a_3}{a_4}{a_5}} .\\ TH1:\,\,\,{a_1} = 2 \Rightarrow {a_1}\,\,co\,1\,\,cach\,\,chon.\\ Gia\,su\,\,{a_2} = 3 \Rightarrow {a_2}\,\,co\,\,1\,\,cach\,\,\,chon.\\ \Rightarrow {a_3}\,\,co\,\,6\,\,cach\,\,chon.\\ {a_4}\,\,co\,\,5\,\,cach\,\,chon.\\ {a_5}\,\,co\,\,4\,\,cach\,\,chon.\\ Tuong\,\,tu\,\,cac\,\,so\,\,{a_3};\,\,{a_4};\,\,{a_{5\,\,}}co\,\,the\,\, = 3\\ \Rightarrow co\,\,\left( {1.1.6.5.4} \right).4 = 480\,\,so\,\,thoa\,\,man.\\ TH2:\,\,{a_1} = 3 \Rightarrow TH\,\,nay\,\,\,tuong\,\,tu\,\,TH1\\ \Rightarrow co\,\,480\,\,so\,\,thoa\,\,man.\\ TH3:\,\,{a_1} \notin \left\{ {2;\,3} \right\} \Rightarrow {a_1}\,\,\,co\,\,5\,\,cach\,\,chon.\\ Gia\,\,su\,\,{a_2},\,\,{a_3} \in \left\{ {2;\,\,3} \right\} \Rightarrow moi\,\,so\,\,\,co\,\,2\,\,cach\,\,chon.\\ Cac\,\,so\,\,con\,\,lai\,\,co\,\,5\,\,cach\,\,chon.\\ \Rightarrow co\,\,5.2.5 = 50\,\,cach\,\,chon.\\ Tuong\,\,tu\,\,ta\,\,co\,\,the\,\,lap\,\,lai\,\,voi\,\,\,\left\{ {{a_2};\,\,{a_4}} \right\} = \left\{ {2;\,\,3} \right\};\,\,\,\left\{ {{a_2};\,\,{a_5}} \right\} = \left\{ {2;\,\,3} \right\};\,\left\{ {{a_3};\,\,{a_4}} \right\} = \left\{ {2;\,\,3} \right\};\,\,\left\{ {{a_3};\,\,{a_5}} \right\} = \left\{ {2;\,\,3} \right\};\,\,\left\{ {{a_4};\,\,{a_5}} \right\} = \left\{ {2;\,\,3} \right\}\\ \Rightarrow co\,\,6.50 = 300\,\,cach\,\,chon.\\ Nhu\,\,vay\,\,co:\,\,480 + 480 + 300 = 1260\,\,so\,\,thoa\,\,man. \end{array}\]