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 girl ? (ii) at least one boy and one girl ? (iii) at least 3 girls ?

Explanation

No girls
Total number of ways the team can have no girls

`=> 4_(C_0)**7_(C_5) =21`

at least one boy and one girl

`=>4_(C_1)**7_(C_4)+4_(C_2)**7_(C_3)+4_(C_3)**7_(C_2)+4_(C_4)**7_(C_1)`

`=>140+210+84+7`

`=>441`

at least 3 girls

`=>4_(C_3)**7_(C_2)+4_(C_4)**7_(C_1)`

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