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

Answer 1

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`