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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 |
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Answer» 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. |
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