(1) \( 1 / 8 \quad \) (2) \( 5 / 8 \quad \) (3) 4/8 (4) \( 7 / 8 \) 10. Keshav has 9 friends, 4 boys and 5 girls. In how many ways can he invite them for birthday party, if there have to be exactly 3 girls in the invitees? (1) \( 120^{\prime \prime} \) (2) 260 (3) 180 (4) 160 (5) None of these

Question

Keshav has 9 friends, 4 boys and 5 girls. In how many ways can he invite them for birthday party, if there have to be exactly 3 girls in the invitees? (1)  120  (2) 260 (3) 180 (4) 160 (5) None of these

Answer 1

Correct option is (4) 160

Keshav can invite exactly 3 girls but he can invite any no. of ways out for 4.

∴ Total no. of ways = \(5_{C_3} (4_{C_0} + 4_{C_1} + 4_{C_2}+ 4_{C_3}+ 4_{C_4})\)

\(= \frac{5\times 4 \times 3!}{2!\times 3!}\times 2^4\)

\(= 10 \times 16\)

\(= 160\)

Hence, Keshav can infinite there friends in 160 ways if there have to be exactly 3 girls in the invitees.