Multiple choice

There are 3 piles of identical red, blue and green balls and each pile contains at least 10 balls. The number of ways of selecting 10 balls, if twice as many red balls as green balls are to be selected, is

  1. 3

  2. 4

  3. 6

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r, b, g be the number of red, blue, and green balls. r + b + g = 10 and r = 2g. Substituting: 2g + b + g = 10, so 3g + b = 10. Since g and b must be non-negative integers: if g=0, b=10; if g=1, b=7; if g=2, b=4; if g=3, b=1. There are 4 possible solutions.

AI explanation

The condition requires selecting twice as many red balls as green balls, giving the relationship R = 2G. The valid non-negative integer combinations of red, green, and blue balls summing to 10 are (0, 0, 10), (2, 1, 7), (4, 2, 4), and (6, 3, 1). Counting these distinct sets gives exactly 4 ways. The result is 4.

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