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  • A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girls (ii) at least one boy and one girl (iii) at least three girls.

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has

(i) no girls
(ii) at least one boy and one girl
(iii) at least three girls.
 

Answers (1)

i.Team having no girls= ^7C_5=\frac{7*6}{2!}=21  

ii.Team having atleast one boy and one girl= ^7C_1*^4C_4+^7C_2*^4C_3+^7C_3*^4C_2+^7C_4*^4C_1=7*1+21*4+35*6+35*4=441  

iii.Team having atleast 3 girls =  ^4C_3*^7C_2+^4C_4*^7C_1=4*21+7=91 

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infoexpert21

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