If the number of ways of selecting K cards out of unlimited number of cards bearing the number 0, 9, 3 so that they can’t be used to write the number 903 is 93, then K is equal to
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We cannot write 903 if in the selection of k cards, we get either (9 or 3), (9 or 0), (0 or 3), (only 0), (only 3), or (only 9).
(9 or 3) can be selected 2 x 2 x 2 .... k times = 2 k times.
Similarly, (9 or 0) or (3 or 0) can be selected 2 k times. In the above selection (only 0) (only 3) or (only 9) is repeated twice.
∴ ∴ Total ways = 3 x 2 k – 3 = 93
⇒ ⇒ k = 5.
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