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Question
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
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`
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