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A debating team consisting of 5 persons is to be chosen from a group of 7 boys and 5...

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roshan-rox | (Level 1) Valedictorian

Posted August 20, 2013 at 5:05 AM via web

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A debating team consisting of 5 persons is to be chosen from a group of 7 boys and 5 girls. In how many ways can this team be formed so that it contains,

(2) at least one girl

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 20, 2013 at 5:55 AM (Answer #1)

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A debating team of 5 persons has to be created from a group of 7 boys and 5 girls.

The number of ways of creating a team with at least one girl is:

C(5, 1)*C(7, 4) + C(5, 2)*C(7, 3) + C(5, 3)*C(7, 2) + C(5, 4)*C(7, 1) + C(5, 5)*C(7, 0)

= 175 + 350 + 210 + 35 + 1

= 771

There are 771 ways of creating a team with at least one girl.

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted August 20, 2013 at 10:55 AM (Answer #2)

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We have 7 boys and 5 girls. So the teams we form can be categorized in to following forms.

  • Teams with girls and boys
  • Teams with only boys
  • Teams with only girls

So except boys only team, every other team has a girl.

Teams containing at least one girl

= Total teams-teams with only boys

`= ^12C_5-^7C_5`

`= 792-21`

`= 771`

So  we can have 771 teams at least a girl included.

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