Question and Answers Forum

All Questions      Topic List

Matrices and Determinants Questions

Previous in All Question      Next in All Question      

Previous in Matrices and Determinants      Next in Matrices and Determinants      

Question Number 55663 by peter frank last updated on 01/Mar/19

Answered by tanmay.chaudhury50@gmail.com last updated on 01/Mar/19

$$b_1{b}_2{b}_3{b}_4{b}_5{b}_6{b}_7{b}_{★}\to b_{★}\to particularboy$$$$group7=b_{★}+2boy+4girl$$$$group7=b_{★}+3b+3g$$$$g7=b_{★}+4b+2g$$$$g7=b_{★}+5b+1g$$$$g7=b_{★}+6b$$$$probablity=$$$$\frac{1c_1\times 7c_2\times 4c_4+1c_1\times 7c_3\times 4c_3+1c_1\times 7c_4\times 4c_2+1c_1\times 7c_5\times 4c_1+1c_1\times 7c_6}{12c_7}$$$$=\frac{21+35\times 4+35\times 6+21\times 4+1\times 7}{\frac{12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2}}$$$$=\frac{21+140+210+84+7}{11\times 9\times 8}$$$$=\frac{462}{11\times 9\times 8}=\frac{42}{9\times 8}$$$$=\frac{14}{3\times 8}$$$$=\frac{7}{12}$$$$plscheckcalculation...$$

Commented by peter frank last updated on 02/Mar/19

$$thankyou$$

Answered by mr W last updated on 02/Mar/19

$$tochoose7membersfrom12persons$$$$therearetotally{C}_7^{12}possibilities.$$$$ifaspecialpersionshouldbeinthe$$$$group,weonlyneedtochoosethe$$$$other6membersfromtheremaining$$$$11persons,thereare{C}_6^{11}possibilities.$$$$\Rightarrow p=\frac{C_6^{11}}{C_7^{12}}=\frac{11!\times 7!\times 5!}{6!\times 5!\times 12!}=\frac{7}{12}$$

Commented by peter frank last updated on 02/Mar/19

$$thankyou$$

Commented by malwaan last updated on 03/Mar/19

$$p=\frac{C_6^{11}}{C_7^{12}}=\frac{\left(11\times 10\times 9\times 8\right)\times 7}{12\times \left(11\times 10\times 9\times 8\right)}=\frac{7}{12}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com