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A Man Has 9 Friends. 4 Boys and 5 Girls. in How Many Ways Can He Invite Them If There Have to Be Exactly 3 Girls in the Invitee'S List? - Mathematics

MCQ

A man has 9 friends. 4 boys and 5 girls. In how many ways can he invite them if there have to be exactly 3 girls in the invitee's list?

Options

  • 320

  • 160

  • 80

  • 200

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Solution

160
Explanation:
Required number of ways

= `""^5C_3+""^5C_3  ""^4C_1+""^5C_3  ""^4C_2+""^5C_3  ""^4C_3+""^5C_3  ""^4C_4 `

= `""^5C_3(1+""^4C_1+""^4C_2+""^4C_3+""^4C_4)`

= `""^5C_3(1+4+6+4+1)`

= `(5!)/(3!  2!)xx16=160`

Concept: Permutation and Combination (Entrance Exam)
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