Combinatorics - Inviting Friends

CAT 1996 Slot 1 · QA · Easy · QA

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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 invitees?

  1. A.

    320

  2. B.

    160

  3. C.

    80

  4. D.

    200

Answer

B

Explanation

Ways to choose 3 girls out of 5 =(53)=10= \binom{5}{3} = 10. Each of the 4 boys can either be invited or not =24=16= 2^4 = 16. Total ways =10×16=160= 10 \times 16 = 160.

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