Multiple choice

The number of ways of selecting 8 balls out of an unlimited number of white, red and blue balls is

  1. 60

  2. 45

  3. 50

  4. 30
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a stars and bars problem: selecting 8 items from 3 categories. Formula: (n+k-1)C(k-1) where n=8, k=3. (8+3-1)C(3-1) = 10C2 = (10*9)/2 = 45.

AI explanation

This problem uses the formula for combinations with repetition, which finds the number of ways to choose r items from n distinct types and is given by (n+r minus 1)Cr. Here, we are selecting 8 balls out of 3 distinct colors (white, red, blue), so n is 3 and r is 8. Plugging the values into the formula gives (3+8 minus 1)C8, which equals 10C8. Since 10C8 is the same as 10C2, the calculation is (10 times 9) divided by (2 times 1), resulting in 45 ways.

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