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Permutation and Combination - General Aptitude

Q1:

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

A 32

B 48

C 64

D 96

E None of these

ANS:C - 64

We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).

 Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
 
= 3 x 6 x 5 + 3 x 2 x 6 + 1
2 x 1 2 x 1
  = (45 + 18 + 1)
  = 64.