A box contains 3 white balls, 4 black balls and 5 yellow balls. In how many ways can 4 balls be drawn so that there is at least one yellow ball.
a) 652 b) 547 c) 425 d) 356 e)None of the above
d)460

• 460 is answer
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• Answer is e
  After solving the value comes 295
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• required no. of ways= total no. of ways of drawing 4 balls- no. of ways of drawing balls such that theres no yellow ball= 12c4-(3c3x5c1+3c2x5c2+3c1x5c3+5c4) =425 ways
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• its d) 460. 12c4 - 7c4 . considering even the same color balls are different. also by
  5c1 x 7c3 + 5c2 x 7c2 + 5c3 x 7c1 + 5c4 x 7c0 = 460
  if same colored balls are identical. then none of the above is correct.
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