Question

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

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (C)

5

Answer 2

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.