Multiple choice

A person gets 9 balls in an event of a festival. He has to put the balls in a basket. To successfully complete the event, he must put more number of balls in the basket than the number of balls which he fails to put. How many number of ways are possible for being him unsuccessful?

  1. 1024

  2. 128

  3. 512

  4. 256

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total outcomes for 9 balls (each can be in or out) is 2^9 = 512. Success means balls in > balls out. Since 9 is odd, there are no ties. By symmetry, half are successes and half are failures. 512 / 2 = 256.

AI explanation

To be unsuccessful, the person must put 4 or fewer balls into the basket while failing to put the remaining 5 or more balls. Since each of the 9 balls has 2 possible outcomes (success or failure in putting it in the basket), we use the fundamental principle of counting. Adding the combinations for putting exactly 0, 1, 2, 3, or 4 balls in the basket gives 1 plus 9 plus 36 plus 84 plus 126, which equals 256 ways.

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