Multiple choice

The number of ways in which one or more balls can be selected out of $10$ white, $9$ green and $7$ blue balls is

  1. $892$
  2. $881$
  3. $891$
  4. $879$
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D Correct answer
Explanation

Total ways to select one or more balls = (10+1)(9+1)(7+1) - 1 = 11 * 10 * 8 - 1 = 880 - 1 = 879.

AI explanation

Since the balls of the same color are identical, the number of green balls chosen can range from 0 to 9, giving 10 choices. Similarly, there are 11 choices for the white balls and 8 choices for the blue balls. Multiplying these gives a total of 880 combinations, but we must subtract the 1 case where zero balls of every color are chosen to satisfy the condition of selecting at least one ball. The result is 879.

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